Results 241 to 250 of about 998,375 (277)

On the ranks of finite simple groups

2016
Summary: Let \(G\) be a finite group and let \(X\) be a conjugacy class of \(G\). The \textit{rank} of \(X\) in \(G\), denoted by \(\operatorname{rank}(G:X)\) is defined to be the minimal number of elements of \(X\) generating \(G\). In this paper we review the basic results on generation of finite simple groups and we survey the recent developments on
Basheer, Ayoub, Moori, Jamshid
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Finite Simple Groups

The American Mathematical Monthly, 1977
(1977). Finite Simple Groups. The American Mathematical Monthly: Vol. 84, No. 9, pp. 693-714.
James F. Hurley, Arunas Rudvalis
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The Classification of the Finite Simple Groups

The Mathematical Intelligencer, 1980
This article on the classification of finite simple groups is directed towards a broad audience. The author poses some natural questions connected with finite groups and in particular with finite simple groups. He explains in a lucid way why these questions have particular answers.
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The periodic groups saturated by finitely many finite simple groups

Siberian Mathematical Journal, 2008
Summary: Denote by \(\mathcal M\) the set whose elements are the simple 3-dimensional unitary groups \(U_3(q)\) and the linear groups \(L_3(q)\) over finite fields. We prove that every periodic group, saturated by the groups of a finite subset of \(\mathcal M\), is finite.
Lytkina, D. V., Tukhvatullina, L. R., Filippov, K. A.   +2 more
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On Some Groups with Finite Involution Saturated with Finite Simple Groups

Mathematical Notes, 2002
By definition, a group \(G\) is saturated with finite simple subgroups if every finite subgroup of \(G\) is contained in a finite simple subgroup of \(G\). An involution \(t\in G\) is said to be finite if, for every \(g\in G\), the subgroup generated by \(t\) and \(t^g\) is finite.
Sozutov, A. I., Shlepkin, A. K.
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Finite simple groups on triple systems

Ars Mathematica Contemporanea, 2023
Summary: Let \(\mathcal{D}\) be a triple system, and let \(G\) be a finite simple group. In this paper we almost determine all possibilities of \(\mathcal{D}\) admitting \(G\) as its flag-transitive automorphism group.
Xiaoqin Zhan, Xuan Pang, Suyun Ding
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2-Signalizers of Finite Simple Groups

Algebra and Logic, 2003
Maximal 2-signalizers and centralizers of Sylow 2-subgroups in all finite simple groups are described. Also normalizers are computed for Sylow 2-subgroups in the finite simple groups of exceptional Lie type over a field of odd characteristic.
Kondrat'ev, A. S., Mazurov, V. D.
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Finite Simple Groups

2003
In a statistical sense, the simple groups (by which we mean, in this window, non-abelian finite simple groups) are quite rare: the Godfather of the subject has likened them to fossils, occasionally found buried among the composition factors of a general finite group [Thompson 1984].
Alexander Lubotzky, Dan Segal
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Computing with finite simple groups

1974
Leech [9] and Birkhoff and Hall [1] are standard references to computational group theory. The lesser-known Petrick [13] contains many articles on symbolic manipulation and group-theoretic work including a description by Sims of techniques he has developed to compute with very large degree permutation groups. These ideas have been used by him [14] most
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Locally Finite Simple Groups

1974
The group G is locally finite if each of its finitely generated subgroups is finite. Until rather recently the area of locally finite groups entirely belonged to the wilderness of counter-examples; and there absurdly wild behaviour is possible, indeed. What little progress has been made in cultivating some fringes of this wilderness is essentially due ...
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