Results 41 to 50 of about 6,369,178 (336)
Simple relations in the Cremona group
, 2010 We give a simple set of generators and relations for the Cremona group of the plane. Namely, we show that the Cremona group is the amalgamated product of the de Jonqui\`eres group with the group of automorphisms of the plane, divided by one relation ...
Blanc, Jérémy
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Finite simple groups as expanders [PDF]
Proceedings of the National Academy of Sciences, 2006 We prove that there exist k ∈ ℕ and 0 < ε ∈ ℝ such that every non-abelian finite simple group G , which is not a Suzuki group, has a set of k generators for which the Cayley graph Cay( G ; S ) is an ε-expander.
Kassabov, M, Lubotzky, A, Nikolov, N
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Finite Groups Isospectral to Simple Groups
Communications in Mathematics and Statistics, 2022 The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum, in particular, to list all finite simple groups for which the recognition problem is solved.
Maria A. Grechkoseeva +4 more
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Classifying cubic symmetric graphs of order 88p and 88p 2
Open MathematicsFor a simple graph Γ\Gamma , Γ\Gamma is said to be ss-regular, provided that the automorphism group of Γ\Gamma regularly acts on the set consisting of ss-arcs of Γ\Gamma .
Zhai Liangliang
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Quasirecognition by prime graph of U_3(q) where 2 < q =p^{alpha} < 100 [PDF]
International Journal of Group Theory, 2012 Let G be a finite group and let Gamma(G) be the prime graphof G. Assume 2 < q = p^{alpha} < 100 . We determine finite groupsG such that Gamma(G) = Gamma(U_3(q)) and prove that if q neq3, 5, 9, 17, then U_3(q) is quasirecognizable by prime graph,i.e., if ...
Ali Iranmanesh +3 more
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OD-characterization of alternating groups Ap+d
Open Mathematics, 2017 Let An be an alternating group of degree n. Some authors have proved that A10, A147 and A189 cannot be OD-characterizable. On the other hand, others have shown that A16, A23+4, and A23+5 are OD-characterizable.
Yang Yong, Liu Shitian, Zhang Zhanghua
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Cohomology of simple modules for algebraic groups
Қарағанды университетінің хабаршысы. Математика сериясы, 2020 In this paper, we consider questions related to the study of the cohomology of simple and simply connected algebraic groups with coefficients in simple modules. There are various calculating methods for them. One of the effective methods is to study the
Sh.Sh. Ibraev +2 more
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A note on finite groups with the indice of some maximal subgroups being primes [PDF]
International Journal of Group Theory, 2017 The Theorem 12 in [A note on $p$-nilpotence and solvability of finite groups, J. Algebra 321 (2009) 1555--1560.] investigated the non-abelian simple groups in which some maximal subgroups have primes indices. In this note we show that this
Cui Zhang
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Group gradings on finitary simple Lie algebras
, 2012 We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically closed field of ...
Bahturin Y. +7 more
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Journal of Algebra, 1977 AbstractRecently, Thompson [9] constructed a new simple group E of order 215 ∘ 3105372 ∘ 13 ∘ 19 ∘ 31 = 90, 745, 943, 887, 872, 000. In particular, E contains only one conjugacy class of involutions, and if e is an involution in E then CE(e) is a (nonsplit) extension of an extra-special 2-group of order 29 by A9, the alternating group of degree 9.The ...
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