Journal articles: 'Solvable groups'

1

Albrecht, Ulrich. "The construction of $A$-solvable Abelian groups." Czechoslovak Mathematical Journal 44, no. 3 (1994): 413–30. http://dx.doi.org/10.21136/cmj.1994.128480.

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2

Cherlin, Gregory L., and Ulrich Felgner. "Homogeneous Solvable Groups." Journal of the London Mathematical Society s2-44, no. 1 (August 1991): 102–20. http://dx.doi.org/10.1112/jlms/s2-44.1.102.

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3

Atanasov, Risto, and Tuval Foguel. "Solitary Solvable Groups." Communications in Algebra 40, no. 6 (June 2012): 2130–39. http://dx.doi.org/10.1080/00927872.2011.574241.

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4

Sarma, B. K. "Solvable fuzzy groups." Fuzzy Sets and Systems 106, no. 3 (September 1999): 463–67. http://dx.doi.org/10.1016/s0165-0114(97)00264-9.

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5

Ray, Suryansu. "Solvable fuzzy groups." Information Sciences 75, no. 1-2 (December 1993): 47–61. http://dx.doi.org/10.1016/0020-0255(93)90112-y.

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6

Chen, P. B., and T. S. Wu. "On solvable groups." Mathematische Annalen 276, no. 1 (March 1986): 43–51. http://dx.doi.org/10.1007/bf01450922.

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7

Abobala, Mohammad, and Mehmet Celik. "Under Solvable Groups as a Novel Generalization of Solvable Groups." Galoitica: Journal of Mathematical Structures and Applications 2, no. 1 (2022): 14–20. http://dx.doi.org/10.54216/gjmsa.020102.

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The objective of this paper is to define a new generalization of solvable groups by using the concept of power maps which generalize the classical concept of powers (exponents). Also, it presents many elementary properties of this new generalization in terms of theorems.

8

GRUNEWALD, FRITZ, BORIS KUNYAVSKII, and EUGENE PLOTKIN. "CHARACTERIZATION OF SOLVABLE GROUPS AND SOLVABLE RADICAL." International Journal of Algebra and Computation 23, no. 05 (August 2013): 1011–62. http://dx.doi.org/10.1142/s0218196713300016.

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We give a survey of new characterizations of finite solvable groups and the solvable radical of an arbitrary finite group which were obtained over the past decade. We also discuss generalizations of these results to some classes of infinite groups and their analogues for Lie algebras. Some open problems are discussed as well.

9

ZARRIN, MOHAMMAD. "GROUPS WITH FEW SOLVABLE SUBGROUPS." Journal of Algebra and Its Applications 12, no. 06 (May 9, 2013): 1350011. http://dx.doi.org/10.1142/s0219498813500114.

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In this paper, we give some sufficient condition on the number of proper solvable subgroups of a group to be nilpotent or solvable. In fact, we show that every group with at most 5 (respectively, 58) proper solvable subgroups is nilpotent (respectively, solvable). Also these bounds cannot be improved.

10

Khazal, R., and N. P. Mukherjee. "A note onp-solvable and solvable finite groups." International Journal of Mathematics and Mathematical Sciences 17, no. 4 (1994): 821–24. http://dx.doi.org/10.1155/s0161171294001158.

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The notion of normal index is utilized in proving necessary and sufficient conditions for a groupGto be respectively,p-solvable and solvable wherepis the largest prime divisor of|G|. These are used further in identifying the largest normalp-solvable and normal solvable subgroups, respectively, ofG.

11

Kirtland, Joseph. "Finite solvable multiprimitive groups." Communications in Algebra 23, no. 1 (January 1995): 335–56. http://dx.doi.org/10.1080/00927879508825224.

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12

Abels, Herbert, and Roger Alperin. "Undistorted solvable linear groups." Transactions of the American Mathematical Society 363, no. 06 (June 1, 2011): 3185. http://dx.doi.org/10.1090/s0002-9947-2011-05237-2.

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13

Rhemtulla, Akbar, and Said Sidki. "Factorizable infinite solvable groups." Journal of Algebra 122, no. 2 (May 1989): 397–409. http://dx.doi.org/10.1016/0021-8693(89)90225-1.

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14

Vesanen, Ari. "Solvable Groups and Loops." Journal of Algebra 180, no. 3 (March 1996): 862–76. http://dx.doi.org/10.1006/jabr.1996.0098.

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15

Budkin, A. I. "Dominions in Solvable Groups." Algebra and Logic 54, no. 5 (November 2015): 370–79. http://dx.doi.org/10.1007/s10469-015-9358-1.

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16

Tent, Joan F. "Quadratic rational solvable groups." Journal of Algebra 363 (August 2012): 73–82. http://dx.doi.org/10.1016/j.jalgebra.2012.04.019.

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17

Timoshenko, E. I. "Universally equivalent solvable groups." Algebra and Logic 39, no. 2 (March 2000): 131–38. http://dx.doi.org/10.1007/bf02681667.

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18

Liu, Yang, and Zi Qun Lu. "Solvable D 2-groups." Acta Mathematica Sinica, English Series 33, no. 1 (August 15, 2016): 77–95. http://dx.doi.org/10.1007/s10114-016-5353-2.

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19

Tyutyunov, V. N. "Characterization ofr-solvable groups." Siberian Mathematical Journal 41, no. 1 (January 2000): 180–87. http://dx.doi.org/10.1007/bf02674008.

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20

CHIODO, MAURICE. "FINITELY ANNIHILATED GROUPS." Bulletin of the Australian Mathematical Society 90, no. 3 (June 13, 2014): 404–17. http://dx.doi.org/10.1017/s0004972714000355.

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AbstractIn 1976, Wiegold asked if every finitely generated perfect group has weight 1. We introduce a new property of groups, finitely annihilated, and show that this might be a possible approach to resolving Wiegold’s problem. For finitely generated groups, we show that in several classes (finite, solvable, free), being finitely annihilated is equivalent to having noncyclic abelianisation. However, we also construct an infinite family of (finitely presented) finitely annihilated groups with cyclic abelianisation. We apply our work to show that the weight of a nonperfect finite group, or a nonperfect finitely generated solvable group, is the same as the weight of its abelianisation. This recovers the known partial results on the Wiegold problem: a finite (or finitely generated solvable) perfect group has weight 1.

21

Sardar, Pranab. "Packing subgroups in solvable groups." International Journal of Algebra and Computation 25, no. 05 (August 2015): 917–26. http://dx.doi.org/10.1142/s0218196715500253.

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We show that any subgroup of a (virtually) nilpotent-by-polycyclic group satisfies the bounded packing property of Hruska–Wise [Packing subgroups in relatively hyperbolic groups, Geom. Topol. 13 (2009) 1945–1988]. In particular, the same is true for all finitely generated subgroups of metabelian groups and linear solvable groups. However, we find an example of a finitely generated solvable group of derived length 3 which admits a finitely generated metabelian subgroup without the bounded packing property. In this example the subgroup is a retract also. Thus we obtain a negative answer to Problem 2.27 of the above paper. On the other hand, we show that polycyclic subgroups of solvable groups satisfy the bounded packing property.

22

Jafarpour, M., H. Aghabozorgi, and B. Davvaz. "Solvable groups derived from hypergroups." Journal of Algebra and Its Applications 15, no. 04 (February 19, 2016): 1650067. http://dx.doi.org/10.1142/s0219498816500675.

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In this paper, we introduce the smallest equivalence relation [Formula: see text] on a hypergroup [Formula: see text] such that the quotient [Formula: see text], the set of all equivalence classes, is a solvable group. The characterization of solvable groups via strongly regular relations is investigated and several results on the topic are presented.

23

Albrecht, Ulrich F. "Extension functors on the category of $A$-solvable abelian groups." Czechoslovak Mathematical Journal 41, no. 4 (1991): 685–94. http://dx.doi.org/10.21136/cmj.1991.102499.

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24

Roman’kov, Vitaly. "Embedding theorems for solvable groups." Proceedings of the American Mathematical Society 149, no. 10 (July 28, 2021): 4133–43. http://dx.doi.org/10.1090/proc/15562.

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In this paper, we prove a series of results on group embeddings in groups with a small number of generators. We show that each finitely generated group G G lying in a variety M {\mathcal M} can be embedded in a 4 4 -generated group H ∈ M A H \in {\mathcal M}{\mathcal A} ( A {\mathcal A} means the variety of abelian groups). If G G is a finite group, then H H can also be found as a finite group. It follows, that any finitely generated (finite) solvable group G G of the derived length l l can be embedded in a 4 4 -generated (finite) solvable group H H of length l + 1 l+1 . Thus, we answer the question of V. H. Mikaelian and A. Yu. Olshanskii. It is also shown that any countable group G ∈ M G\in {\mathcal M} , such that the abelianization G a b G_{ab} is a free abelian group, is embeddable in a 2 2 -generated group H ∈ M A H\in {\mathcal M}{\mathcal A} .

25

Dymarz, Tullia. "Envelopes of certain solvable groups." Commentarii Mathematici Helvetici 90, no. 1 (2015): 195–224. http://dx.doi.org/10.4171/cmh/351.

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26

Rogers, Pat, Howard Smith, and Donald Solitar. "Tarski's Problem for Solvable Groups." Proceedings of the American Mathematical Society 96, no. 4 (April 1986): 668. http://dx.doi.org/10.2307/2046323.

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27

Roman’kov, V. A. "Algorithmic theory of solvable groups." Prikladnaya Diskretnaya Matematika, no. 52 (2021): 16–64. http://dx.doi.org/10.17223/20710410/52/2.

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The purpose of this survey is to give some picture of what is known about algorithmic and decision problems in the theory of solvable groups. We will provide a number of references to various results, which are presented without proof. Naturally, the choice of the material reported on reflects the author’s interests and many worthy contributions to the field will unfortunately go without mentioning. In addition to achievements in solving classical algorithmic problems, the survey presents results on other issues. Attention is paid to various aspects of modern theory related to the complexity of algorithms, their practical implementation, random choice, asymptotic properties. Results are given on various issues related to mathematical logic and model theory. In particular, a special section of the survey is devoted to elementary and universal theories of solvable groups. Special attention is paid to algorithmic questions regarding rational subsets of groups. Results on algorithmic problems related to homomorphisms, automorphisms, and endomorphisms of groups are presented in sufficient detail.

28

Mohammadzadeh, F., and Elahe Mohammadzadeh. "On $\alpha$-solvable fundamental groups." Journal of Algebraic Hyperstructures and Logical Algebras 2, no. 2 (May 1, 2021): 35–46. http://dx.doi.org/10.52547/hatef.jahla.2.2.35.

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29

SUZUKI, Michio. "Solvable Generation of Finite Groups." Hokkaido Mathematical Journal 16, no. 1 (February 1987): 109–13. http://dx.doi.org/10.14492/hokmj/1381517825.

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30

Meierfrankenfeld, Ulrich, Richard E. Phillips, and Orazio Puglisi. "Locally Solvable Finitary Linear Groups." Journal of the London Mathematical Society s2-47, no. 1 (February 1993): 31–40. http://dx.doi.org/10.1112/jlms/s2-47.1.31.

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31

Farrell, F. Thomas, and Peter A. Linnell. "K-Theory of Solvable Groups." Proceedings of the London Mathematical Society 87, no. 02 (September 2003): 309–36. http://dx.doi.org/10.1112/s0024611503014072.

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32

Pál, Hegedus. "Structure of solvable rational groups." Proceedings of the London Mathematical Society 90, no. 02 (February 25, 2005): 439–71. http://dx.doi.org/10.1112/s0024611504015035.

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33

Snow, Dennis M. "Complex orbits of solvable groups." Proceedings of the American Mathematical Society 110, no. 3 (March 1, 1990): 689. http://dx.doi.org/10.1090/s0002-9939-1990-1028050-9.

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34

Edidin, Dan, and William Graham. "Good representations and solvable groups." Michigan Mathematical Journal 48, no. 1 (2000): 203–13. http://dx.doi.org/10.1307/mmj/1030132715.

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35

Emmanouil, Ioannis. "Solvable groups and Bass' conjecture." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 326, no. 3 (February 1998): 283–87. http://dx.doi.org/10.1016/s0764-4442(97)82981-3.

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36

OSIN, D. V. "The entropy of solvable groups." Ergodic Theory and Dynamical Systems 23, no. 3 (June 2003): 907–18. http://dx.doi.org/10.1017/s0143385702000937.

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37

Li, Cai Heng, and Lei Wang. "Finite REA-groups are solvable." Journal of Algebra 522 (March 2019): 195–217. http://dx.doi.org/10.1016/j.jalgebra.2018.11.033.

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38

Deshpande, Tanmay. "Minimal idempotents on solvable groups." Selecta Mathematica 22, no. 3 (March 19, 2016): 1613–61. http://dx.doi.org/10.1007/s00029-016-0229-y.

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39

Wolter, T. H. "Einstein Metrics on solvable groups." Mathematische Zeitschrift 206, no. 1 (January 1991): 457–71. http://dx.doi.org/10.1007/bf02571355.

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40

TANAKA, Yasuhiko. "Amalgams of quasithin solvable groups." Japanese journal of mathematics. New series 17, no. 2 (1991): 203–66. http://dx.doi.org/10.4099/math1924.17.203.

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41

Arazy, Jonathan, and Harald Upmeier. "Berezin Transform for Solvable Groups." Acta Applicandae Mathematicae 81, no. 1 (March 2004): 5–28. http://dx.doi.org/10.1023/b:acap.0000024192.68563.8d.

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42

HILLMAN, JONATHAN A. "2-KNOTS WITH SOLVABLE GROUPS." Journal of Knot Theory and Its Ramifications 20, no. 07 (July 2011): 977–94. http://dx.doi.org/10.1142/s021821651100898x.

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We show that fibered 2-knots with closed fiber the Hantzsche–Wendt flat 3-manifold are not reflexive, while every fibered 2-knot with closed fiber a Nil-manifold with base orbifold S(3, 3, 3) is reflexive. We also determine when the knots are amphicheiral or invertible, and give explicit representatives for the possible meridians (up to automorphisms of the knot group which induce the identity on abelianization) for the groups of all knots in either class. This completes the TOP classification of 2-knots with torsion-free, elementary amenable knot group. In the final section, we show that the only non-trivial doubly null-concordant knots with such groups are those with the group of the 2-twist spin of the knot 946.

43

Isaacs, I. M., and Geoffrey R. Robinson. "Isomorphic subgroups of solvable groups." Proceedings of the American Mathematical Society 143, no. 8 (April 23, 2015): 3371–76. http://dx.doi.org/10.1090/proc/12534.

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44

Rogers, Pat, Howard Smith, and Donald Solitar. "Tarski’s problem for solvable groups." Proceedings of the American Mathematical Society 96, no. 4 (April 1, 1986): 668. http://dx.doi.org/10.1090/s0002-9939-1986-0826500-0.

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45

Garreta, Albert, Alexei Miasnikov, and Denis Ovchinnikov. "Diophantine problems in solvable groups." Bulletin of Mathematical Sciences 10, no. 01 (February 21, 2020): 2050005. http://dx.doi.org/10.1142/s1664360720500058.

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We study the Diophantine problem (decidability of finite systems of equations) in different classes of finitely generated solvable groups (nilpotent, polycyclic, metabelian, free solvable, etc.), which satisfy some natural “non-commutativity” conditions. For each group [Formula: see text] in one of these classes, we prove that there exists a ring of algebraic integers [Formula: see text] that is interpretable in [Formula: see text] by finite systems of equations ([Formula: see text]-interpretable), and hence that the Diophantine problem in [Formula: see text] is polynomial time reducible to the Diophantine problem in [Formula: see text]. One of the major open conjectures in number theory states that the Diophantine problem in any such [Formula: see text] is undecidable. If true this would imply that the Diophantine problem in any such [Formula: see text] is also undecidable. Furthermore, we show that for many particular groups [Formula: see text] as above, the ring [Formula: see text] is isomorphic to the ring of integers [Formula: see text], so the Diophantine problem in [Formula: see text] is, indeed, undecidable. This holds, in particular, for free nilpotent or free solvable non-abelian groups, as well as for non-abelian generalized Heisenberg groups and uni-triangular groups [Formula: see text]. Then, we apply these results to non-solvable groups that contain non-virtually abelian maximal finitely generated nilpotent subgroups. For instance, we show that the Diophantine problem is undecidable in the groups [Formula: see text].

46

Turull, Alexandre. "Character correspondences in solvable groups." Journal of Algebra 295, no. 1 (January 2006): 157–78. http://dx.doi.org/10.1016/j.jalgebra.2005.01.028.

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47

Myasnikov, A., and N. Romanovskiy. "Krull dimension of solvable groups." Journal of Algebra 324, no. 10 (November 2010): 2814–31. http://dx.doi.org/10.1016/j.jalgebra.2010.07.013.

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48

Isaacs, I. M. "Solvable groups contain large centralizers." Israel Journal of Mathematics 55, no. 1 (February 1986): 58–64. http://dx.doi.org/10.1007/bf02772695.

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49

Navarro, Gabriel, Alexandre Turull, and Thomas R. Wolf. "Block separation in solvable groups." Archiv der Mathematik 85, no. 4 (October 2005): 293–96. http://dx.doi.org/10.1007/s00013-005-1407-x.

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50

Crestani, Eleonora, and Andrea Lucchini. "Normal coverings of solvable groups." Archiv der Mathematik 98, no. 1 (November 29, 2011): 13–18. http://dx.doi.org/10.1007/s00013-011-0341-3.

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Journal articles on the topic 'Solvable groups'

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