Journal articles: 'Group F(2'

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Akhmedov, Azer, Melanie Stein, and Jennifer Taback. "Free limits of Thompson’s group F." Geometriae Dedicata 155, no. 1 (January 29, 2011): 163–76. http://dx.doi.org/10.1007/s10711-011-9583-2.

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KOBERDA, THOMAS, and YASH LODHA. "2-chains and square roots of Thompson’s group." Ergodic Theory and Dynamical Systems 40, no. 9 (March 25, 2019): 2515–32. http://dx.doi.org/10.1017/etds.2019.14.

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We study 2-generated subgroups $\langle f,g\rangle <\operatorname{Homeo}^{+}(I)$ such that $\langle f^{2},g^{2}\rangle$ is isomorphic to Thompson’s group $F$, and such that the supports of $f$ and $g$ form a chain of two intervals. We show that this class contains uncountably many isomorphism types. These include examples with non-abelian free subgroups, examples which do not admit faithful actions by $C^{2}$ diffeomorphisms on 1-manifolds, examples which do not admit faithful actions by $PL$ homeomorphisms on an interval, and examples which are not finitely presented. We thus answer questions due to Brin. We also show that many relatively uncomplicated groups of homeomorphisms can have very complicated square roots, thus establishing the behavior of square roots of $F$ as part of a general phenomenon among subgroups of $\operatorname{Homeo}^{+}(I)$.

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BAMBERG, JOHN, SAUL D. FREEDMAN, and LUKE MORGAN. "ON -GROUPS WITH AUTOMORPHISM GROUPS RELATED TO THE CHEVALLEY GROUP." Journal of the Australian Mathematical Society 108, no. 3 (January 8, 2020): 321–31. http://dx.doi.org/10.1017/s1446788719000466.

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Let $p$ be an odd prime. We construct a $p$-group $P$ of nilpotency class two, rank seven and exponent $p$, such that $\text{Aut}(P)$ induces $N_{\text{GL}(7,p)}(G_{2}(p))=Z(\text{GL}(7,p))G_{2}(p)$ on the Frattini quotient $P/\unicode[STIX]{x1D6F7}(P)$. The constructed group $P$ is the smallest $p$-group with these properties, having order $p^{14}$, and when $p=3$ our construction gives two nonisomorphic $p$-groups. To show that $P$ satisfies the specified properties, we study the action of $G_{2}(q)$ on the octonion algebra over $\mathbb{F}_{q}$, for each power $q$ of $p$, and explore the reducibility of the exterior square of each irreducible seven-dimensional $\mathbb{F}_{q}[G_{2}(q)]$-module.

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Fiore, Marcelo, and Tom Leinster. "An abstract characterization of Thompson’s group F." Semigroup Forum 80, no. 2 (January 23, 2010): 325–40. http://dx.doi.org/10.1007/s00233-010-9209-2.

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Chaudhry, Humayun J., Paul E. Schoch, and Burke A. Cunha. "Flavimonas oryzihabitans (CDC Group Ve-2)." Infection Control & Hospital Epidemiology 13, no. 8 (August 1992): 485–88. http://dx.doi.org/10.1086/646578.

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Flavimonas oryzihabitansis an uncommon organism with distinctive microbiological and biochemical features that is infrequently isolated from humans. The presence of foreign material, including indwelling intravascular catheters and artificial grafts, or various surgical procedures appear to predispose patients with underlying disease to bacteremic infection withFlavimonas. A gram-negative bacillus,F oryzihabitansis sensitive to most antibiotics except first- and second-generation cephalosporins.F oryzihabitansisolated from blood should be considered pathogenic in patients with indwelling catheters or prosthetic materials.Previously designatedPseudomonas oryzihabitansand also known as Centers for Disease Control (CDC) Group Ve-2,F oryzihabitansis an unusual gram-negative, nonfermenting, oxidase-negative bacillus that is uncommonly associated with serious illness in humans.’ First described by Dresel and Stickl in 1928 and initially assigned the nameBacterium typhiflavumbecause of its similarity to the typhoid bacillus, the organism has been isolated from a variety of human sources, including blood, wounds, and abscesses, and (in mixed cultures) from sputum, urine, and cervical cultures.

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Feshchenko, Bohdan. "Deformations of smooth functions on 2-torus." Proceedings of the International Geometry Center 12, no. 3 (December 1, 2019): 30–50. http://dx.doi.org/10.15673/tmgc.v12i3.1528.

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Let $f$ be a Morse function on a smooth compact surface $M$ and $\mathcal{S}'(f)$ be the group of $f$-preserving diffeomorphisms of $M$ which are isotopic to the identity map. Let also $G(f)$ be a group of automorphisms of the Kronrod-Reeb graph of $f$ induced by elements from $\mathcal{S}'(f)$, and $\Delta'$ be the subgroup of $\mathcal{S}'(f)$ consisting of diffeomorphisms which trivially act on the graph of $f$ and are isotopic to the identity map. The group $\pi_0\mathcal{S}'(f)$ can be viewed as an analogue of a mapping class group for $f$-preserved diffeomorphisms of $M$. The groups $\pi_0\Delta'(f)$ and $G(f)$ encode ``combinatorially trivial'' and ``combinatorially nontrivial'' counterparts of $\pi_0\mathcal{S}'(f)$ respectively. In the paper we compute groups $\pi_0\mathcal{S}'(f)$, $G(f)$, and $\pi_0\Delta'(f)$ for Morse functions on $2$-torus $T^2$.

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Gogineni, V. K., and A. Modrykamien. "Lung Abscesses in 2 Patients With Lancefield Group F Streptococci (Streptococcus milleri Group)." Respiratory Care 56, no. 12 (December 1, 2011): 1966–69. http://dx.doi.org/10.4187/respcare.01316.

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Deaconescu, Marian. "On a special class of finite 2-groups." Glasgow Mathematical Journal 34, no. 1 (January 1992): 127–31. http://dx.doi.org/10.1017/s0017089500008624.

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In the course of classifying those finite groups F which have exactly five maximal subgroups, R. W. van der Waall [4] proved that one encounters the following situation. One class of such groups F is described by F = SP, where S = O2(F)∈Syl2(F), P ∈ Syl3(F), S/Φ(S) ≅ Z2 × Z2, P is cyclic and P operates via conjugation on 5 as a group of order 3, because in this case F/Φ(F) ≅ A4.

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Brown, Kenneth A. "Class groups and automorphism groups of group rings." Glasgow Mathematical Journal 28, no. 1 (January 1986): 79–86. http://dx.doi.org/10.1017/s0017089500006376.

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This paper is a sequel to [2]. A polycyclic-by-finite group G was there called dihedral free if G contains no subgroup isomorphic to 〈b, a:ba = b-1 a2 = 1〉 whose normalizer has finite index in G. It was shown in [2, Theorem F] that, if R is a commutative Noetherian domain, the group ring RG is a prime Noetherian maximal order if and only if R is integrally closed, G is dihedral free, and G has no non-trivial finite normal subgroups. Throughout, R and G will be assumed to satisfy these hypotheses. The main aim of the paper is to study the class group of the maximal order RG.

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Li, Yufang, and Zhe Dong. "P-Tensor Product for Group C*-Algebras." Mathematics 8, no. 4 (April 18, 2020): 627. http://dx.doi.org/10.3390/math8040627.

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In this paper, we introduce new tensor products ⊗ p ( 1 ≤ p ≤ + ∞ ) on C ℓ p * ( Γ ) ⊗ C ℓ p * ( Γ ) and ⊗ c 0 on C c 0 * ( Γ ) ⊗ C c 0 * ( Γ ) for any discrete group Γ . We obtain that for 1 ≤ p < + ∞ C ℓ p * ( Γ ) ⊗ m a x C ℓ p * ( Γ ) = C ℓ p * ( Γ ) ⊗ p C ℓ p * ( Γ ) if and only if Γ is amenable; C c 0 * ( Γ ) ⊗ m a x C c 0 * ( Γ ) = C c 0 * ( Γ ) ⊗ c 0 C c 0 * ( Γ ) if and only if Γ has Haagerup property. In particular, for the free group with two generators F 2 we show that C ℓ p * ( F 2 ) ⊗ p C ℓ p * ( F 2 ) ≇ C ℓ q * ( F 2 ) ⊗ q C ℓ q * ( F 2 ) for 2 ≤ q < p ≤ + ∞ .

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Zaman, Nabil, and Nicholas Pippenger. "ASYMPTOTIC ANALYSIS OF OPTIMAL NESTED GROUP-TESTING PROCEDURES." Probability in the Engineering and Informational Sciences 30, no. 4 (June 29, 2016): 547–52. http://dx.doi.org/10.1017/s0269964816000267.

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We analyze a construction for optimal nested group-testing procedures, and show that, when individuals are independently positive with probability p, the expected number of tests per positive individual, F*(p), has, as p→0, the asymptotic behavior $$F^{\ast}(p) = \log_2 {1\over p} + \log_2 \log 2 + 2 + f\left(\log_2 {1\over p} + \log_2 \log 2\right) + O(p),$$ where $$f(z) = 4\times 2^{-2^{1-\{z\}}} - \{z\} - 1,$$ and {z}=z−⌊z⌋ is the fractional part of z. The function f(z) is a periodic function (with period 1) that exhibits small oscillations (with magnitude <0.005) about an even smaller average value (<0.0005).

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Vignéras, Marie-France. "Representations modulo p of the p-adic group GL(2, F)." Compositio Mathematica 140, no. 02 (March 2004): 333–58. http://dx.doi.org/10.1112/s0010437x03000071.

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Gildea, Joe. "The structure of the unit group of the group algebra $\mathbb{F}_{2^k } A_4 $." Czechoslovak Mathematical Journal 61, no. 2 (June 2011): 531–39. http://dx.doi.org/10.1007/s10587-011-0071-5.

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Gildea, Joe, Rhian Taylor, Abidin Kaya, and A. Tylyshchak. "Double bordered constructions of self-dual codes from group rings over Frobenius rings." Cryptography and Communications 12, no. 4 (January 9, 2020): 769–84. http://dx.doi.org/10.1007/s12095-019-00420-3.

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AbstractIn this work, we describe a double bordered construction of self-dual codes from group rings. We show that this construction is effective for groups of order 2p where p is odd, over the rings $\mathbb {F}_{2}+u\mathbb {F}_{2}$ F 2 + u F 2 and $\mathbb {F}_{4}+u\mathbb {F}_{4}$ F 4 + u F 4 . We demonstrate the importance of this new construction by finding many new binary self-dual codes of lengths 64, 68 and 80; the new codes and their corresponding weight enumerators are listed in several tables.

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Li, Shangzhi. "Overgroups of a unitary group in GL(2, K)." Journal of Algebra 149, no. 2 (July 1992): 275–86. http://dx.doi.org/10.1016/0021-8693(92)90016-f.

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Formichella, Marc, R. M. Green, and Eric Stade. "Coxeter group actions on 4 F 3(1) hypergeometric series." Ramanujan Journal 24, no. 1 (November 25, 2010): 93–128. http://dx.doi.org/10.1007/s11139-010-9253-2.

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Bullett, Shaun, and Luna Lomonaco. "Mating quadratic maps with the modular group II." Inventiones mathematicae 220, no. 1 (October 10, 2019): 185–210. http://dx.doi.org/10.1007/s00222-019-00927-9.

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Abstract In 1994 S. Bullett and C. Penrose introduced the one complex parameter family of (2 : 2) holomorphic correspondences $$\mathcal {F}_a$$Fa: $$\begin{aligned} \left( \frac{aw-1}{w-1}\right) ^2+\left( \frac{aw-1}{w-1}\right) \left( \frac{az+1}{z+1}\right) +\left( \frac{az+1}{z+1}\right) ^2=3 \end{aligned}$$aw-1w-12+aw-1w-1az+1z+1+az+1z+12=3and proved that for every value of $$a \in [4,7] \subset \mathbb {R}$$a∈[4,7]⊂R the correspondence $$\mathcal {F}_a$$Fa is a mating between a quadratic polynomial $$Q_c(z)=z^2+c,\,\,c \in \mathbb {R}$$Qc(z)=z2+c,c∈R, and the modular group $$\varGamma =PSL(2,\mathbb {Z})$$Γ=PSL(2,Z). They conjectured that this is the case for every member of the family $$\mathcal {F}_a$$Fa which has a in the connectedness locus. We show here that matings between the modular group and rational maps in the parabolic quadratic family $$Per_1(1)$$Per1(1) provide a better model: we prove that every member of the family $$\mathcal {F}_a$$Fa which has a in the connectedness locus is such a mating.

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Kravchenko, Anna, and Sergiy Maksymenko. "Automorphisms of Kronrod-Reeb graphs of Morse functions on 2-sphere." Proceedings of the International Geometry Center 11, no. 4 (April 4, 2019): 72–79. http://dx.doi.org/10.15673/tmgc.v11i4.1306.

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Let $M$ be a compact two-dimensional manifold and, $f \in C^{\infty}(M, R)$ be a Morse function, and $\Gamma$ be its Kronrod-Reeb graph.Denote by $O(f)={f o h | h \in D(M)}$ the orbit of $f$ with respect to the natural right action of the group of diffeomorphisms $D(M)$ onC^{\infty}$, and by $S(f)={h\in D(M) | f o h = f }$ the coresponding stabilizer of this function.It is easy to show that each $h\in S(f)$ induces an automorphism of the graph $\Gamma$.Let $D_{id}(M)$ be the identity path component of $D(M)$, $S'(f) = S(f) \cap D_{id}(M)$ be the subgroup of $D_{id}(M)$ consisting of diffeomorphisms preserving $f$ and isotopic to identity map, and $G$ be the group of automorphisms of the Kronrod-Reeb graph induced by diffeomorphisms belonging to $S'(f)$. This group is one of key ingredients for calculating the homotopy type of the orbit $O(f)$. In the previous article the authors described the structure of groups $G$ for Morse functions on all orientable surfacesdistinct from $2$-torus and $2$-sphere. The present paper is devoted to the case $M = S^2$. In this situation $\Gamma$ is always a tree, and therefore all elements of the group $G$ have a common fixed subtree $Fix(G)$, which may even consist of a unique vertex. Our main result calculates the groups $G$ for all Morse functions $f: S^2 \to R$ whose fixed subtree $Fix(G)$ consists of more than one point.

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James, Colin. "Commentary on `Power, Institution and Group-Analytic Training' by Robert F. Marten (Group Analysis 32(2))." Group Analysis 32, no. 3 (September 1999): 460–62. http://dx.doi.org/10.1177/0533316499323016.

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James, C. "Commentary on 'Power, Institution and Group-Analytic Training' by Robert F. Marten (Group Analysis 32(2))." Group Analysis 32, no. 3 (September 1, 1999): 460–62. http://dx.doi.org/10.1177/05333169922076798.

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Inkster, James A. H., Didier J. Colin, and Yann Seimbille. "A novel 2-cyanobenzothiazole-based 18F prosthetic group for conjugation to 1,2-aminothiol-bearing targeting vectors." Organic & Biomolecular Chemistry 13, no. 12 (2015): 3667–76. http://dx.doi.org/10.1039/c4ob02637c.

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[¹⁸F]FPyPEGCBT is a new ¹⁸F labelling agent which contains a 2-substituted pyridine for incorporation of [¹⁸F]F⁻ and a 2-cyanobenzothiazole moiety for chemo-selective conjugation to 1,2-aminothiol-bearing biomolecules.

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Ivanov, Sergei O., and Roman Mikhailov. "On discrete homology of a free pro--group." Compositio Mathematica 154, no. 10 (September 7, 2018): 2195–204. http://dx.doi.org/10.1112/s0010437x1800739x.

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For a prime $p$, let $\hat{F}_{p}$ be a finitely generated free pro-$p$-group of rank at least $2$. We show that the second discrete homology group $H_{2}(\hat{F}_{p},\mathbb{Z}/p)$ is an uncountable $\mathbb{Z}/p$-vector space. This answers a problem of A. K. Bousfield.

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Holt, Derek F. "An Alternative Proof That the Fibonacci Group F(2, 9) is Infinite." Experimental Mathematics 4, no. 2 (January 1995): 97–100. http://dx.doi.org/10.1080/10586458.1995.10504312.

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Kulikova, O. V. "On the conjugacy problem in the group F/N 1 ∩ N 2." Mathematical Notes 93, no. 5-6 (May 2013): 837–49. http://dx.doi.org/10.1134/s0001434613050234.

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Akhlaghi, Z., M. Khatami, and B. Khosravi. "Quasirecognition by prime graph of the simple group 2 F 4(q)." Acta Mathematica Hungarica 122, no. 4 (January 26, 2009): 387–97. http://dx.doi.org/10.1007/s10474-009-8048-7.

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EL-Fassi, Iz-iddine, and Samir Kabbaj. "The hyperstability of AQ-Jensen functional equation on 2-divisible abelian group and inner product spaces." Annals of West University of Timisoara - Mathematics and Computer Science 53, no. 2 (December 1, 2015): 59–72. http://dx.doi.org/10.1515/awutm-2015-0014.

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Abstract In this paper, we prove the hyperstability of the following mixed additive-quadratic-Jensen functional equation $$2f({{x + y} \over 2}) + f({{x - y} \over 2}) + f({{y - x} \over 2}) = f(x) + f(y)$$ in the class of functions from an 2-divisible abelian group G into a Banach space.

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Brophy, Alfred L. "Educational Level, Occupation, and the MMPI-2 F-K Index." Psychological Reports 77, no. 1 (August 1995): 175–78. http://dx.doi.org/10.2466/pr0.1995.77.1.175.

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The relationship between the F-K dissimulation index and educational and occupational level was examined in the MMPI-2 normative group. Higher levels of education and occupation are associated with higher scores on the K scale and with lower scores on the F scale and the F-K index. Mean F-K scores differ by 5 to 7 points between the lowest and highest educational and occupational levels, necessitating consideration of those factors when interpreting the index. The effects of education and occupation on the F-K index are similar for men and women in the MMPI-2 normative group.

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Aslan, Tuǧba, and Pál Hegedüs. "Maximal deviation of large powers in the Nottingham group." Journal of Group Theory 22, no. 3 (May 1, 2019): 397–418. http://dx.doi.org/10.1515/jgth-2018-0133.

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Abstract The group of formal power series under substitution over {\mathbb{F}_{p}} , the so-called Nottingham group, is a pro-p group so it is a metric space. The intertwining of these two structures is an important object of study. This paper is concerned with how the power map influences the distance of elements. Suppose that {d(f,\,g)=d_{1}} while {d(f,1)=d_{2}\geq d_{1}} . In this paper we provide a sharp bound for {d(f^{j},\,g^{j})} in terms of {d_{1},\,d_{2}} and the exponent j. This bound confirms a conjecture by K. Keating.

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GURJAR, R. V., and SAGAR KOLTE. "FUNDAMENTAL GROUP OF SOME GENUS-2 FIBRATIONS AND APPLICATIONS." International Journal of Mathematics 23, no. 08 (July 10, 2012): 1250080. http://dx.doi.org/10.1142/s0129167x12500802.

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We will prove that given a genus-2 fibration f : X → C on a smooth projective surface X such that b1(X) = b1(C) + 2, the fundamental group of X is almost isomorphic to π1(C) × π1(E), where E is an elliptic curve. We will also verify the Shafarevich Conjecture on holomorphic convexity of the universal cover of surfaces X with genus-2 fibration X → C such that b1(X) > b1(C).

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CHEN, JIECHENG, DASHAN FAN, and FAYOU ZHAO. "BOCHNER–RIESZ MEANS ON BLOCK-SOBOLEV SPACES IN COMPACT LIE GROUP." Journal of the Australian Mathematical Society 109, no. 2 (January 8, 2020): 176–92. http://dx.doi.org/10.1017/s1446788719000430.

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On a compact Lie group $G$ of dimension $n$, we study the Bochner–Riesz mean $S_{R}^{\unicode[STIX]{x1D6FC}}(f)$ of the Fourier series for a function $f$. At the critical index $\unicode[STIX]{x1D6FC}=(n-1)/2$, we obtain the convergence rate for $S_{R}^{(n-1)/2}(f)$ when $f$ is a function in the block-Sobolev space. The main theorems extend some known results on the $m$-torus $\mathbb{T}^{m}$.

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Pangestuti, Riana Wibi, Mungin Eddy Wibowo, and Muhammad Japar. "The Effectiveness of Psychoeducational Group with Group Exercises Technique to Improve Student’s Self-Efficacy." Islamic Guidance and Counseling Journal 3, no. 1 (January 30, 2020): 38–45. http://dx.doi.org/10.25217/igcj.v3i1.673.

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Self-efficacy is a determining factor to achieve the learning objectives. Therefore, self-efficacy is important to be measured and improved. This study aimed to examine the effectiveness of a psychoeducational group with exercises techniques to improve students’ self-efficacy. This study was carried out by using a pretest-posttest control group design by involving 2 groups, the experimental and control group. The data from these groups were analyzed using repeated-measure MIX MANOVA. Meanwhile, the authors used self-efficacy scale (α=0.911) to collect the data of 14 students. The results showed that there were effects of time in the improvement of students' self-efficacy (F(2)=1,746; p<0.05), group members effect (F(3,984)=8,442; p<0.05), and the effect of time interacting with group members (F(1,293)=0.045; p<0.05). It can be concluded that the psychoeducational group with exercises techniques is effective to improve students’ self-efficacy by regarding the duration of intervention, group member, and time interaction with group members. This study implication to the guidance and counseling services will be discussed.

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Purdy, Andrew P., and Ray J. Butcher. "Tetrakis[μ2-1,1,1,3,3,3-hexafluoro-2-(trifluoromethyl)propan-2-olato]tetrakis(μ3-2-methylpropan-2-olato)octacopper(I)." Acta Crystallographica Section E Crystallographic Communications 77, no. 6 (May 28, 2021): 668–71. http://dx.doi.org/10.1107/s2056989021005429.

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The title compound, [Cu8(C4H9O)4(C4F9O)4], crystallizes in the monoclinic space group, P21/n and contains a self-assembly of two C16H18Cu4F18O4 units linked by bridging tert-butyl groups [Cu—O bonds of length 2.3779 (15) and 2.4248 (15) Å], generating a centrosymmetric dimer. The asymmetrical unit, C16H18Cu4F18O4, contains an almost square-planar arrangement of the four Cu atoms linked by bridging tert-butyl and perfluorinated tert-butyl groups with Cu—Cu distances ranging from 2.7108 (4) to 2.7612 (4) Å and Cu —Cu—Cu angle values close to 90° [ranging from 89.459 (10)° to 90.025 (11)°]. These dimers are further linked by weak C—H...F and F...F interactions. As is commonly encountered in perfluorinated tert-butyl groups, one of the CF3 groups is disordered and was refined with two equivalent conformations with occupancies of 0.74 (3) and 0.26 (3).

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Crabb, M. J., and C. M. McGregor. "Faithful, irreducible *-representations for group algebras of free products." Proceedings of the Edinburgh Mathematical Society 42, no. 3 (October 1999): 559–74. http://dx.doi.org/10.1017/s0013091500020526.

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Let G be the free product of groups A and B, where |A|≥3 and |B|≥2. We construct faithful, irreducible *-representations for the group algebras ℂ[G] and ℓ1(G). The construction gives a faithful, irreducible representation for F[G] when the field F does not have characteristic 2.

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Shanbhag, Niraj M., Michael D. Geschwind, John J. DiGiovanna, Catherine Groden, Rena Godfrey, Matthew J. Yousefzadeh, Erin A. Wade, et al. "Neurodegeneration as the presenting symptom in 2 adults with xeroderma pigmentosum complementation group F." Neurology Genetics 4, no. 3 (June 2018): e240. http://dx.doi.org/10.1212/nxg.0000000000000240.

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ObjectiveTo describe the features of 2 unrelated adults with xeroderma pigmentosum complementation group F (XP-F) ascertained in a neurology care setting.MethodsWe report the clinical, imaging, molecular, and nucleotide excision repair (NER) capacity of 2 middle-aged women with progressive neurodegeneration ultimately diagnosed with XP-F.ResultsBoth patients presented with adult-onset progressive neurologic deterioration involving chorea, ataxia, hearing loss, cognitive deficits, profound brain atrophy, and a history of skin photosensitivity, skin freckling, and/or skin neoplasms. We identified compound heterozygous pathogenic mutations in ERCC4 and confirmed deficient NER capacity in skin fibroblasts from both patients.ConclusionsThese cases illustrate the role of NER dysfunction in neurodegeneration and how adult-onset neurodegeneration could be the major symptom bringing XP-F patients to clinical attention. XP-F should be considered by neurologists in the differential diagnosis of patients with adult-onset progressive neurodegeneration accompanied by global brain atrophy and a history of heightened sun sensitivity, excessive freckling, and skin malignancies.

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Yamuna, Thammarse S., Jerry P. Jasinski, Brian J. Anderson, H. S. Yathirajan, and Manpreet Kaur. "2-[4-(Trifluoromethyl)phenylsulfanyl]benzoic acid." Acta Crystallographica Section E Structure Reports Online 69, no. 11 (October 26, 2013): o1704. http://dx.doi.org/10.1107/s1600536813028778.

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In the title compound, C14H9F3O2S, the dihedral angle between the mean planes of the benzene rings is 88.7 (2)°. The carboxylic acid group is twisted by 13.6 (7)° from the mean plane of its attached aromatic ring. One of the F atoms of the trifluoromethyl group is disordered over two sites in a 0.61 (7):0.39 (7) ratio. In the crystal, inversion dimers linked by pairs of O—H...O hydrogen bonds generateR22(8) loops. Weak C—H...F interactions are also observed.

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Bahturin, Y. A., and A. Giambruno. "Group Gradings on Associative Algebras with Involution." Canadian Mathematical Bulletin 51, no. 2 (June 1, 2008): 182–94. http://dx.doi.org/10.4153/cmb-2008-020-7.

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AbstractIn this paper we describe the group gradings by a finite abelian group G of the matrix algebra Mn(F) over an algebraically closed field F of characteristic different from 2, which respect an involution (involution gradings). We also describe, under somewhat heavier restrictions on the base field, all G-gradings on all finite-dimensional involution simple algebras.

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BALOGH, ZSOLT, and YUANLIN LI. "ON THE DERIVED LENGTH OF THE GROUP OF UNITS OF A GROUP ALGEBRA." Journal of Algebra and Its Applications 06, no. 06 (December 2007): 991–99. http://dx.doi.org/10.1142/s0219498807002624.

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Ciobotaru, Corina. "Parabolically induced unitary representations of the universal group $U(F)^+$ are $C_0$." MATHEMATICA SCANDINAVICA 125, no. 1 (August 29, 2019): 113–34. http://dx.doi.org/10.7146/math.scand.a-114722.

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We prove that all parabolically induced unitary representations of the Burger-Mozes universal group $U(F)^{+}$, with $F$ being primitive, are $C_0$. This generalizes the same well-known result for the universal group $U(F)^{+}$, when $F$ is $2$-transitive.

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BARANOV, A. A., and I. D. SUPRUNENKO. "MODULAR BRANCHING RULES FOR 2-COLUMN DIAGRAM REPRESENTATIONS OF GENERAL LINEAR GROUPS." Journal of Algebra and Its Applications 04, no. 05 (October 2005): 489–515. http://dx.doi.org/10.1142/s0219498805001356.

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In this paper branching rules for the polynomial irreducible representations of the general linear groups in positive characteristic with highest weights labeled by partitions of the form (2a, 1b, 0c) and their restrictions to the special linear groups are found. The submodule structure of the restrictions of the corresponding irreducible modules for the group GLn(F) (or SLn(F)) to the naturally embedded subgroup GLn-1(F) (or SLn-1(F)) is determined. As a corollary, inductive systems of irreducible representations for GL∞(F) and SL∞(F) that consist of representations indicated above, are classified. The submodule structure of the relevant Weyl modules is refined.

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Dubcovsky, Jorge, and Arturo Martínez. "Phenetic relationships in the Festuca spp. from Patagonia." Canadian Journal of Botany 66, no. 3 (March 1, 1988): 468–78. http://dx.doi.org/10.1139/b88-072.

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Forty-two anatomical and exomorphological characters from 16 species and 2 varieties of Festuca native from Patagonia were numerically analyzed. Principal components analysis together with cluster analysis arranged 14 taxa into 5 groups (F. tunicata and F. acanthophylla, group 1; F. monticola, F. thermarum, and F. scabriuscula, group 2; F. pallescens, F. p. var. scabra, and F. kurtziana, group 3; F. gracillima and F. ventanicola, group 4; and F. contracta, F. rubra var. simpliciuscula, F. pyrogea, and F. magellanica, group 5; F. argentina, F. purpurascens, F. cirrosa and F. pampeana were not included in any of the groups). Cluster analyses performed on either vegetative or reproductive characters showed that they alone are not enough to summarize variation among these taxa.

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Awtrey, Chad, and Peter Jakes. "Galois Groups of Even Sextic Polynomials." Canadian Mathematical Bulletin 63, no. 3 (December 12, 2019): 670–76. http://dx.doi.org/10.4153/s0008439519000754.

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AbstractLet $f(x)=x^{6}+ax^{4}+bx^{2}+c$ be an irreducible sextic polynomial with coefficients from a field $F$ of characteristic $\neq 2$, and let $g(x)=x^{3}+ax^{2}+bx+c$. We show how to identify the conjugacy class in $S_{6}$ of the Galois group of $f$ over $F$ using only the discriminants of $f$ and $g$ and the reducibility of a related sextic polynomial. We demonstrate that our method is useful for producing one-parameter families of even sextic polynomials with a specified Galois group.

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42

Stöhr, Ralph. "On elements of order four in certain free central extensions of groups." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 1 (July 1989): 13–28. http://dx.doi.org/10.1017/s0305004100067955.

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Let F be a non-cyclic free group, R a normal subgroup of F and G = F/R, i.e.where π is the natural projection of F onto G, is a free presentation of G. Let R′ denote the commutator subgroup of R. The quotient F/[R′,F] is a free central extensionof the group F/R′, the latter being a free abelianized extension of G. While F/R′ is torsion-free (see, e.g. [2], p. 23), elements of finite order may occur in R′/[R′,F], the kernel of the free central extension (l·2). Since C. K. Gupta [1] discovered elements of order 2 in the free centre-by-metabelian group F/[F″,F] (i.e. (1·2) in the case R = F′), torsion in F/[R′,F] has been studied by a number of authors (see, e.g. [4–13]). Clearly the elements of finite order in F/[R′,F] form a subgroup T of the abelian group R′/[R′,F]. It will be convenient to write T additively. By a result of Kuz'min [5], any element of T has order 2 or 4. Moreover, it was pointed out in [5] that elements of order 4 may really occur. On the other hand, it has been shown in [11] that, if G has no 2-torsion, then T is an elementary abelian 2-group isomorphic to H4(G, ℤ2). So if T contains an element of order 4, then G must have 2-torsion. We also mention a result of Zerck [13], who proved that 2T is an invariant of G, i.e. it does not depend on the particular choice of the free presentation (1·1).

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Rutter, N. "Proposed projects—Working group 2, interlaken workshop for past global changes." Global and Planetary Change 2, no. 1-2 (May 1990): 87–95. http://dx.doi.org/10.1016/0921-8181(90)90039-f.

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Gekeler, Ernst-Ulrich. "Para-Eisenstein Series for the Modular Group $GL(2, \mathbb{F}_q[T])$." Taiwanese Journal of Mathematics 15, no. 4 (August 2011): 1463–75. http://dx.doi.org/10.11650/twjm/1500406358.

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Lazic, Biljana, Thomas Armbruster, Christian Chopin, Edward S. Grew, Alain Baronnet, and Lukas Palatinus. "Superspace description of wagnerite-group minerals (Mg,Fe,Mn)2(PO4)(F,OH)." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 70, no. 2 (March 4, 2014): 243–58. http://dx.doi.org/10.1107/s2052520613031247.

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Reinvestigation of more than 40 samples of minerals belonging to the wagnerite group (Mg, Fe, Mn)2(PO4)(F,OH) from diverse geological environments worldwide, using single-crystal X-ray diffraction analysis, showed that most crystals have incommensurate structures and, as such, are not adequately described with known polytype models (2b), (3b), (5b), (7b) and (9b). Therefore, we present here a unified superspace model for the structural description of periodically and aperiodically modulated wagnerite with the (3+1)-dimensional superspace groupC2/c(0β0)s0 based on the average triplite structure with cell parametersa≃ 12.8,b≃ 6.4,c≃ 9.6 Å, β ≃ 117° and the modulation vectorsq=βb*. The superspace approach provides a way of simple modelling of the positional and occupational modulation of Mg/Fe and F/OH in wagnerite. This allows direct comparison of crystal properties.

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Hu, Guangming, Yutong Liu, Yu Sun, and Xinjie Qian. "Carleson Measure of Harmonic Schwarzian Derivatives Associated with a Finitely Generated Fuchsian Group of the Second Kind." Journal of Function Spaces 2021 (March 20, 2021): 1–6. http://dx.doi.org/10.1155/2021/5523454.

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Let S H f be the Schwarzian derivative of a univalent harmonic function f in the unit disk D , compatible with a finitely generated Fuchsian group G of the second kind. We show that if S H f 2 1 − z 2 3 d x d y satisfies the Carleson condition on the infinite boundary of the Dirichlet fundamental domain F of G , then S H f 2 1 − z 2 3 d x d y is a Carleson measure in D .

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Meakin, John, and Nóra Szakács. "Inverse monoids and immersions of 2-Complexes." International Journal of Algebra and Computation 25, no. 01n02 (February 2015): 301–23. http://dx.doi.org/10.1142/s0218196715400123.

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It is well known that under mild conditions on a connected topological space 𝒳, connected covers of 𝒳 may be classified via conjugacy classes of subgroups of the fundamental group of 𝒳. In this paper, we extend these results to the study of immersions into two-dimensional CW-complexes. An immersion f : 𝒟 → 𝒞 between CW-complexes is a cellular map such that each point y ∈ 𝒟 has a neighborhood U that is mapped homeomorphically onto f(U) by f. In order to classify immersions into a two-dimensional CW-complex 𝒞, we need to replace the fundamental group of 𝒞 by an appropriate inverse monoid. We show how conjugacy classes of the closed inverse submonoids of this inverse monoid may be used to classify connected immersions into the complex.

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You, Hong, and Xuemei Zhou. "Maps Preserving Commutators on the Standard Borel Subgroup of the Unitary Group over a Field." Algebra Colloquium 23, no. 03 (June 20, 2016): 507–18. http://dx.doi.org/10.1142/s1005386716000493.

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Let F be a field with char F ≠ 2 and |F| > 9, and let B 2n(F) be the standard Borel subgroup of the unitary group U 2n(F) over F. For n ≥ 3, we obtain a complete description of all bijective maps preserving commutators on B 2n(F).

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Herfort, Wolfgang N., Luis Ribes, and Pavel A. Zalesskii. "Fixed Points of Automorphisms of Free Pro-p Groups of Rank 2." Canadian Journal of Mathematics 47, no. 2 (April 1, 1995): 383–404. http://dx.doi.org/10.4153/cjm-1995-021-6.

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AbstractLet p be a prime number, and let F be a free pro-p group of rank two. Consider an automorphism α of F of finite order m, and let FixF(α) = {x ∈ F | α(x) = x} be the subgroup of F consisting of the elements fixed by α. It is known that if m is prime to p and α = idF, then the rank of FixF(α) is infinite. In this paper we show that if m is a finite power pr of p, the rank of FixF(α) is at most 2. We conjecture that if the rank of F is n and the order of a is a power of α, then rank (FixF(α)) ≤ n.

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Brauckmann, Boris. "The 2-Sylow-Subgroup of the Tame Kernel of Number Fields." Canadian Journal of Mathematics 43, no. 2 (April 1, 1991): 255–64. http://dx.doi.org/10.4153/cjm-1991-014-x.

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For a number field F with ring of integers OF the tame symbols yield a surjective homomorphism with a finite kernel, which is called the tame kernel, isomorphic to K2(OF). For the relative quadratic extension E/F, where and E ≠ F, let CS(E/ F)(2) denote the 2-Sylow-subgroup of the relative S-class-group of E over F, where S consists of all infinite and dyadic primes of F, and let m be the number of dyadic primes of F, which decompose in E.

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Journal articles on the topic 'Group F(2'

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