Relevant bibliographies by topics / Finite groups

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Finite groups'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 August 2024

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Journal articles on the topic "Finite groups"

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A. Jund, Asaad, and Haval M. Mohammed Salih. "Result Involution Graphs of Finite Groups." Journal of Zankoy Sulaimani - Part A 23, no. 1 (June 20, 2021): 113–18. http://dx.doi.org/10.17656/jzs.10846.

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Zhang, Jinshan, Zhencai Shen, and Jiangtao Shi. "Finite groups with few vanishing elements." Glasnik Matematicki 49, no. 1 (June 8, 2014): 83–103. http://dx.doi.org/10.3336/gm.49.1.07.

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Kondrat'ev, A. S., A. A. Makhnev, and A. I. Starostin. "Finite groups." Journal of Soviet Mathematics 44, no. 3 (February 1989): 237–318. http://dx.doi.org/10.1007/bf01676868.

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Andruskiewitsch, N., and G. A. García. "Extensions of Finite Quantum Groups by Finite Groups." Transformation Groups 14, no. 1 (November 18, 2008): 1–27. http://dx.doi.org/10.1007/s00031-008-9039-4.

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Conrad, Paul F., and Jorge Martinez. "Locally finite conditions on lattice-ordered groups." Czechoslovak Mathematical Journal 39, no. 3 (1989): 432–44. http://dx.doi.org/10.21136/cmj.1989.102314.

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Chen, Yuanqian, Paul Conrad, and Michael Darnel. "Finite-valued subgroups of lattice-ordered groups." Czechoslovak Mathematical Journal 46, no. 3 (1996): 501–12. http://dx.doi.org/10.21136/cmj.1996.127311.

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Kniahina, V. N., and V. S. Monakhov. "Finite groups with semi-subnormal Schmidt subgroups." Algebra and Discrete Mathematics 29, no. 1 (2020): 66–73. http://dx.doi.org/10.12958/adm1376.

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Cao, Jian Ji, and Xiu Yun Guo. "Finite NPDM-groups." Acta Mathematica Sinica, English Series 37, no. 2 (February 2021): 306–14. http://dx.doi.org/10.1007/s10114-021-8047-3.

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Burn, R. P., L. C. Grove, and C. T. Benson. "Finite Reflection Groups." Mathematical Gazette 70, no. 451 (March 1986): 77. http://dx.doi.org/10.2307/3615867.

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Stonehewer, S. E. "FINITE SOLUBLE GROUPS." Bulletin of the London Mathematical Society 25, no. 5 (September 1993): 505–6. http://dx.doi.org/10.1112/blms/25.5.505.

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Dissertations / Theses on the topic "Finite groups"

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Mkiva, Soga Loyiso Tiyo. "The non-cancellation groups of certain groups which are split extensions of a finite abelian group by a finite rank free abelian group." Thesis, University of the Western Cape, 2008. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_8520_1262644840.

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The groups we consider in this study belong to the class X0 of all finitely generated groups with finite commutator subgroups.

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Marion, Claude Miguel Emmanuel. "Triangle groups and finite simple groups." Thesis, Imperial College London, 2009. http://hdl.handle.net/10044/1/4371.

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This thesis contains a study of the spaces of homomorphisms from hyperbolic triangle groups to finite groups of Lie type which leads to a number of deterministic, asymptotic,and probabilistic results on the (p1, p2, p3)-generation problem for finite groups of Lie type. Let G₀ = L(pn) be a finite simple group of Lie type over the finite field Fpn and let T = Tp1,p2,p3 be the hyperbolic triangle group (x,y : xp1 = yp2 = (xy)p3 = 1) where p1, p2, p3 are prime numbers satisfying the hyperbolic condition 1/p1 + 1/p2 + 1/p3 < 1. In general, the size of Hom(T,G₀) is a polynomial in q, where q = pn, whose degree gives the dimension of Hom(T,G), where G is the corresponding algebraic group, seen as a variety. Computing the precise size of Hom(T,G₀) or giving an asymptotic estimate leads to a number of applications. One can for example investigate whether or not there is an epimorphism in Hom(T,G₀). This is equivalent to determining whether or not G₀ is a (p1, p2, p3)-group. Asymptotically, one might be interested in determining the probability that a random homomorphism in Hom(T,G₀) is an epimorphism as |G₀|→∞ . Given a prime number p, one can also ask wether there are finitely, or infinitely many positive integers n such that L(pn) is a (p1, p2, p3)-group. We solve these problems for the following families of finite simple groups of Lie type of small rank: the classical groups PSL2(q), PSL3(q), PSU3(q) and the exceptional groups 2B2(q), 2G2(q), G2(q), 3D4(q). The methods involve the character theory and the subgroup structure of these groups. Following the concept of linear rigidity of a triple of elements in GLn(Fp), used in inverse Galois theory, we introduce the concept for a hyperbolic triple of primes to be rigid in a simple algebraic group G. The triple (p1, p2, p3) is rigid in G if the sum of the dimensions of the subvarieties of elements of order p1, p2, p3 in G is equal to 2 dim G. This is the minimum required for G(pn) to have a generating triple of elements of these orders. We formulate a conjecture that if (p1, p2, p3) is a rigid triple then given a prime p there are only finitely many positive integers n such that L(pn) is a (p1, p2, p3)-group. We prove this conjecture for the classical groups PSL2(q), PSL3(q), and PSU3(q) and show that it is consistent with the substantial results in the literature about Hurwitz groups (i.e. when (p1, p2, p3) = (2, 3, 7)). We also classify the rigid hyperbolic triples of primes in algebraic groups, and in doing so we obtain some new families of non-Hurwitz groups.
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George, Timothy Edward. "Symmetric representation of elements of finite groups." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3105.

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The purpose of the thesis is to give an alternative and more efficient method for working with finite groups by constructing finite groups as homomorphic images of progenitors. The method introduced can be applied to all finite groups that possess symmetric generating sets of involutions. Such groups include all finite non-abelian simple groups, which can then be constructed by the technique of manual double coset enumeration.
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Wegner, Alexander. "The construction of finite soluble factor groups of finitely presented groups and its application." Thesis, University of St Andrews, 1992. http://hdl.handle.net/10023/12600.

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Computational group theory deals with the design, analysis and computer implementation of algorithms for solving computational problems involving groups, and with the applications of the programs produced to interesting questions in group theory, in other branches of mathematics, and in other areas of science. This thesis describes an implementation of a proposal for a Soluble Quotient Algorithm, i.e. a description of the algorithms used and a report on the findings of an empirical study of the behaviour of the programs, and gives an account of an application of the programs. The programs were used for the construction of soluble groups with interesting properties, e.g. for the construction of soluble groups of large derived length which seem to be candidates for groups having efficient presentations. New finite soluble groups of derived length six with trivial Schur multiplier and efficient presentations are described. The methods for finding efficient presentations proved to be only practicable for groups of moderate order. Therefore, for a given derived length soluble groups of small order are of interest. The minimal soluble groups of derived length less than or equal to six are classified.
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Bujard, Cédric. "Finite subgroups of the extended Morava stabilizer groups." Thesis, Strasbourg, 2012. http://www.theses.fr/2012STRAD010/document.

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L'objet de la thèse est la classification à conjugaison près des sous-groupes finis du groupe de stabilisateur (classique) de Morava S_n et du groupe de stabilisateur étendu G_n(u) associé à une loi de groupe formel F de hauteur n définie sur le corps F_p à p éléments. Une classification complète dans S_n est établie pour tout entier positif n et premier p. De plus, on montre que la classification dans le groupe étendu dépend aussi de F et son unité associée u dans l'anneau des entiers p-adiques. On établit un cadre théorique pour la classification dans G_n(u), on donne des conditions nécessaires et suffisantes sur n, p et u pour l'existence dans G_n(u) d'extensions de sous-groupes finis maximaux de S_n par le groupe de Galois de F_{p^n} sur F_p, et lorsque de telles extensions existent on dénombre leurs classes de conjugaisons. On illustre nos méthodes en fournissant une classification complète et explicite dans le cas n=2
The problem addressed is the classification up to conjugation of the finite subgroups of the (classical) Morava stabilizer group S_n and the extended Morava stabilizer group G_n(u) associated to a formal group law F of height n over the field F_p of p elements. A complete classification in S_n is provided for any positive integer n and prime p. Furthermore, we show that the classification in the extended group also depends on F and its associated unit u in the ring of p-adic integers. We provide a theoretical framework for the classification in G_n(u), we give necessary and sufficient conditions on n, p and u for the existence in G_n(u) of extensions of maximal finite subgroups of S_n by the Galois group of F_{p^n} over F_p, and whenever such extension exist we enumerate their conjugacy classes. We illustrate our methods by providing a complete and explicit classification in the case n=2
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McDougall-Bagnall, Jonathan M. "Generation problems for finite groups." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/2529.

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It can be deduced from the Burnside Basis Theorem that if G is a finite p-group with d(G)=r then given any generating set A for G there exists a subset of A of size r that generates G. We have denoted this property B. A group is said to have the basis property if all subgroups have property B. This thesis is a study into the nature of these two properties. Note all groups are finite unless stated otherwise. We begin this thesis by providing examples of groups with and without property B and several results on the structure of groups with property B, showing that under certain conditions property B is inherited by quotients. This culminates with a result which shows that groups with property B that can be expressed as direct products are exactly those arising from the Burnside Basis Theorem. We also seek to create a class of groups which have property B. We provide a method for constructing groups with property B and trivial Frattini subgroup using finite fields. We then classify all groups G where the quotient of G by the Frattini subgroup is isomorphic to this construction. We finally note that groups arising from this construction do not in general have the basis property. Finally we look at groups with the basis property. We prove that groups with the basis property are soluble and consist only of elements of prime-power order. We then exploit the classification of all such groups by Higman to provide a complete classification of groups with the basis property.
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Menezes, Nina E. "Random generation and chief length of finite groups." Thesis, University of St Andrews, 2013. http://hdl.handle.net/10023/3578.

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Part I of this thesis studies P[subscript(G)](d), the probability of generating a nonabelian simple group G with d randomly chosen elements, and extends this idea to consider the conditional probability P[subscript(G,Soc(G))](d), the probability of generating an almost simple group G by d randomly chosen elements, given that they project onto a generating set of G/Soc(G). In particular we show that for a 2-generated almost simple group, P[subscript(G,Soc(G))](2) 53≥90, with equality if and only if G = A₆ or S₆. Furthermore P[subscript(G,Soc(G))](2) 9≥10 except for 30 almost simple groups G, and we specify this list and provide exact values for P[subscript(G,Soc(G))](2) in these cases. We conclude Part I by showing that for all almost simple groups P[subscript(G,Soc(G))](3)≥139/150. In Part II we consider a related notion. Given a probability ε, we wish to determine d[superscript(ε)] (G), the number of random elements needed to generate a finite group G with failure probabilty at most ε. A generalisation of a result of Lubotzky bounds d[superscript(ε)](G) in terms of l(G), the chief length of G, and d(G), the minimal number of generators needed to generate G. We obtain bounds on the chief length of permutation groups in terms of the degree n, and bounds on the chief length of completely reducible matrix groups in terms of the dimension and field size. Combining these with existing bounds on d(G), we obtain bounds on d[superscript(ε)] (G) for permutation groups and completely reducible matrix groups.
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JÃnior, Raimundo de AraÃjo Bastos. "Commutators in finite groups." Universidade Federal do CearÃ, 2010. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=5496.

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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
Os problemas que abordaremos estÃo diretamente associados à existÃncia de elementos no subgrupo derivado que nÃo sÃo comutadores. Nosso objetivo serà apresentar os resultados de Tim Bonner, que sÃo estimativas para a razÃo entre o comprimento do derivado e a ordem do grupo (limitaÃÃo superior e determinaÃÃo do "comportamento assintÃtico"), culminando com uma prova da conjectura de Bardakov.
The problems which we address in this work are directly related to the existence of elements in the derived subgroup that are not commutators. Our purpose is to present the results of Tim Bonner [1]. In his paper, one finds estimates for the ratio between the commutator length and the order of group (more precisely, upper limits and the establishment of its asymptotic behavior), leading to the proof of Bardakov's Conjecture.
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Stavis, Andreas. "Representations of finite groups." Thesis, Karlstads universitet, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-69642.

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Representation theory is concerned with the ways of writing elements of abstract algebraic structures as linear transformations of vector spaces. Typical structures amenable to representation theory are groups, associative algebras and Lie algebras. In this thesis we study linear representations of finite groups. The study focuses on character theory and how character theory can be used to extract information from a group. Prior to that, concepts needed to treat character theory, and some of their ramifications, are investigated. The study is based on existing literature, with excessive use of examples to illuminate important aspects. An example treating a class of p-groups is also discussed.
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Torres, Bisquertt María de la Luz. "Symmetric generation of finite groups." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2625.

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Advantages of the double coset enumeration technique include its use to represent group elements in a convenient shorter form than their usual permutation representations and to find nice permutation representations for groups. In this thesis we construct, by hand, several groups, including U₃(3) : 2, L₂(13), PGL₂(11), and PGL₂(7), represent their elements in the short form (symmetric representation) and produce their permutation representations.
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Books on the topic "Finite groups"

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Hartley, B., G. M. Seitz, A. V. Borovik, and R. M. Bryant, eds. Finite and Locally Finite Groups. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0329-9.

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C, Grove Larry, ed. Finite reflection groups. 2nd ed. New York: Springer-Verlag, 1985.

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Oliver, Robert. Whitehead groups of finite groups. Cambridge: Cambridge University Press, 1988.

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Grove, L. C., and C. T. Benson. Finite Reflection Groups. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4757-1869-0.

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Sengupta, Ambar N. Representing Finite Groups. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1231-1.

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Grove, Larry C. Finite reflection groups. 2nd ed. New York: Springer-Verlag, 1985.

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Grove, Larry C. Finite reflection groups. 2nd ed. New York: Springer, 1996.

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1936-, Hawkes Trevor O., ed. Finite soluble groups. Berlin: W. de Gruyter, 1992.

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Blichfeldt, Hans Frederick. Finite collineation groups: With an introduction to the theory of operators and substitution groups. [sl]: [Lindemann Press], 2010.

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Griess, Robert L. Twelve sporadic groups. Berlin: Springer, 1998.

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Book chapters on the topic "Finite groups"

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Saxl, J. "Finite Simple Groups and Permutation Groups." In Finite and Locally Finite Groups, 97–110. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0329-9_4.

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Seitz, G. M. "Algebraic Groups." In Finite and Locally Finite Groups, 45–70. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0329-9_2.

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Zalesskiĭ, A. E. "Group Rings of Simple Locally Finite Groups." In Finite and Locally Finite Groups, 219–46. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0329-9_9.

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Brešar, Matej. "Finite Groups." In Springer Undergraduate Mathematics Series, 223–50. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-14053-3_6.

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Georgi, Howard. "Finite Groups." In Lie Algebras in Particle Physics, 2–42. Boca Raton: CRC Press, 2018. http://dx.doi.org/10.1201/9780429499210-2.

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Rosebrock, Stephan. "Finite Groups." In Springer Undergraduate Mathematics Series, 127–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 2024. http://dx.doi.org/10.1007/978-3-662-69365-0_7.

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Shalev, A. "Finite p-Groups." In Finite and Locally Finite Groups, 401–50. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0329-9_15.

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Grove, L. C., and C. T. Benson. "Coxeter Groups." In Finite Reflection Groups, 34–52. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4757-1869-0_4.

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Hartley, B. "Simple Locally Finite Groups." In Finite and Locally Finite Groups, 1–44. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0329-9_1.

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Kurzweil, Hans, and Bernd Stellmacher. "Groups Acting on Groups." In The Theory of Finite Groups, 175–223. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/0-387-21768-1_8.

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Conference papers on the topic "Finite groups"

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Kakarala, Ramakrishna. "Bispectrum on finite groups." In ICASSP 2009 - 2009 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2009. http://dx.doi.org/10.1109/icassp.2009.4960328.

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Qin, Yongbin, Haiyue Zhang, and Daoyun Xu. "Constructions of Finite Groups." In 2015 International Conference on Computer Science and Intelligent Communication. Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/csic-15.2015.85.

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PASSMAN, D. S. "SEMIPRIMITIVITY OF GROUP ALGEBRAS OF LOCALLY FINITE GROUPS." In Proceedings of the AMS Special Session. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814503723_0008.

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GREUEL, GERT-MARTIN, and GERHARD PFISTER. "COMPUTER ALGEBRA AND FINITE GROUPS." In Proceedings of the First International Congress of Mathematical Software. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777171_0002.

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Swathi, V. V., and M. S. Sunitha. "Square graphs of finite groups." In INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCES-MODELLING, COMPUTING AND SOFT COMPUTING (CSMCS 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0045744.

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Casazza, Peter G., and Matthew Fickus. "Chirps on finite cyclic groups." In Optics & Photonics 2005, edited by Manos Papadakis, Andrew F. Laine, and Michael A. Unser. SPIE, 2005. http://dx.doi.org/10.1117/12.618272.

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Castellani, L. "Differential calculi on finite groups." In Corfu Summer Institute on Elementary Particle Physics. Trieste, Italy: Sissa Medialab, 1999. http://dx.doi.org/10.22323/1.001.0069.

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Sims, Charles C. "Computing with subgroups of automorphism groups of finite groups." In the 1997 international symposium. New York, New York, USA: ACM Press, 1997. http://dx.doi.org/10.1145/258726.258857.

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Babai, L., and L. Ronyai. "Computing irreducible representations of finite groups." In 30th Annual Symposium on Foundations of Computer Science. IEEE, 1989. http://dx.doi.org/10.1109/sfcs.1989.63461.

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MALININ, D. "ON INTEGRAL REPRESENTATIONS OF FINITE GROUPS." In Proceedings of the Conference. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814350051_0018.

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Reports on the topic "Finite groups"

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Holmes, Richard B. Signal Processing on Finite Groups. Fort Belvoir, VA: Defense Technical Information Center, February 1990. http://dx.doi.org/10.21236/ada221129.

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Elkholy, Abd-Elmoneim Mohamed, Mohamed Hussein Hafez Abd-ellatif, and Sarah Hassan El-sherif. Influence of S-permutable GS-subgroups on Finite Groups. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, July 2019. http://dx.doi.org/10.7546/crabs.2019.07.01.

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Zhai, Liangliang, and Xuanlong Ma. Perfect Codes in Proper Order Divisor Graphs of Finite Groups. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, December 2020. http://dx.doi.org/10.7546/crabs.2020.12.04.

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Moradipour, Kayvan. Conjugacy Class Sizes and n-th Commutativity Degrees of Some Finite Groups. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, May 2018. http://dx.doi.org/10.7546/crabs.2018.04.02.

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Wang, Yao, Jeehee Lim, Rodrigo Salgado, Monica Prezzi, and Jeremy Hunter. Pile Stability Analysis in Soft or Loose Soils: Guidance on Foundation Design Assumptions with Respect to Loose or Soft Soil Effects on Pile Lateral Capacity and Stability. Purdue University, 2022. http://dx.doi.org/10.5703/1288284317387.

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The design of laterally loaded piles is often done in practice using the p-y method with API p-y curves representing the behavior of soil at discretized points along the pile length. To account for pile-soil-pile interaction in pile groups, AASHTO (2020) proposes the use of p-multipliers to modify the p-y curves. In this research, we explored, in depth, the design of lateral loaded piles and pile groups using both the Finite Element (FE) method and the p-y method to determine under what conditions pile stability problems were likely to occur. The analyses considered a wide range of design scenarios, including pile diameters ranging from 0.36 m (14.17 inches) to 1.0 m (39.37 inches), pile lengths ranging from 10 m (32.81 ft) to 20 m (65.62 ft), uniform and multilayered soil profiles containing weak soil layers of loose sand or normally consolidated (NC) clay, lateral load eccentricity ranging from 0 m to 10 m (32.81 ft), combined axial and lateral loads, three different pile group configurations (1×5, 2×5, and 3×5), pile spacings ranging from 3 to 5 times the pile diameter, two different load directions (“strong” direction and “weak” direction), and two different pile cap types (free-standing and soil-supported pile caps). Based on the FEA results, we proposed new p-y curve equations for clay and sand. We also examined the behavior of the individual piles in the pile groups and found that the moment applied to the pile cap is partly transferred to the individual piles as moments, which is contrary to the assumption often made that moments are fully absorbed by axial loads on the group piles. This weakens the response of the piles to lateral loading because a smaller lateral pressure is required to produce a given deflection when moments are transferred to the head of the piles as moments. When the p-y method is used without consideration of the transferred moments, unconservative designs result. Based on the FEA results, we proposed both a new set of p-multipliers and a new method to use when moment distribution between piles is not known, using pile efficiency instead to calculate the total capacity of pile groups.
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Cho, Yong Seung. Finite Group Actions in Seiberg–Witten Theory. GIQ, 2012. http://dx.doi.org/10.7546/giq-8-2007-135-143.

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Liu, Xiu, and Xuanlong Ma. The Order Divisor Graph of a Finite Group. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, March 2020. http://dx.doi.org/10.7546/crabs.2020.03.06.

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8

Sitek, M., C. Bojanowski, A. Bergeron, and J. Licht. Involute Working Group – FSI Analysis of Fuel Plates Using Finite Volume and Finite Element Methods. Office of Scientific and Technical Information (OSTI), November 2021. http://dx.doi.org/10.2172/1845461.

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Jaegers, Peter James. Lie group invariant finite difference schemes for the neutron diffusion equation. Office of Scientific and Technical Information (OSTI), June 1994. http://dx.doi.org/10.2172/10165908.

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Li, Huani, Xuanlong Ma, and Ruiqin Fu. The Probability that a Subgroup of a Finite Group Is Characteristic. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, September 2021. http://dx.doi.org/10.7546/crabs.2021.09.01.

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