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Finite Simple Groups

Finite simple groups of low rank‎: ‎Hurwitz generation and $(2,3)$-generation

Finite simple groups of low rank‎: ‎Hurwitz generation and $(2,3)$-generation

... when finite) is a group generated by an involution and an element of order 3, whose product has order ...Such groups have been studied intensively, starting from the pioneering works of Hurwitz [7] and ...

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Finite simple groups with number of zeros slightly greater than the number of nonlinear irreducible characters

Finite simple groups with number of zeros slightly greater than the number of nonlinear irreducible characters

... FINITE SIMPLE GROUPS WITH NUMBER OF ZEROS SLIGHTLY GREATER THAN THE NUMBER OF NONLINEAR IRREDUCIBLE CHARACTERS.. GUANGJU ZENG.[r] ...

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Finite simple groups which are the products of symmetric or alternating groups with $L_{3}(4)$

Finite simple groups which are the products of symmetric or alternating groups with $L_{3}(4)$

... In this paper, all groups considered are finite. By definition, a group G is called factorizable if G = AB for some proper subgroups A and B of G, otherwise it is called non-factorizable. The subgroups A ...

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Quasirecognition by prime graph of finite simple groups ${}^2D_n(3)$

Quasirecognition by prime graph of finite simple groups ${}^2D_n(3)$

... Proof. By assumption, from [11, Tables 6, 8] we deduce that t(D) ≥ 4, since n ≥ 4. Also ρ(2, D) = {2, r 2n } and so t(2, D) ≥ 2. Now by Lemma 2.1, it follows that there exists a finite nonabelian simple ...

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Finite groups with the same conjugacy class sizes as a finite simple group

Finite groups with the same conjugacy class sizes as a finite simple group

... Thompson’s conjecture for some finite simple groups has been studied . In [9], A. Camina and R. Camina asked about the structure of a group with the same cs as a simple group. In the other ...

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Progenitors Related to Simple Groups

Progenitors Related to Simple Groups

... all finite simple groups. The composition factors of a finite group allow us to view our group as a product of its simple ...the finite group. By completing the double coset ...

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Centralizers in simple locally finite groups

Centralizers in simple locally finite groups

... Abstract. This is a survey article on centralizers of finite subgroups in locally finite, simple groups or LFS-groups as we will call them. We mention some of the open problems about ...

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Finite groups of the same type as Suzuki groups

Finite groups of the same type as Suzuki groups

... two groups G and H are of the same type, then nse(G) = nse(H) and |G| = ...non-solvable groups, in particular, finite simple ...studied finite simple groups whose order is ...

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A Simple Classification of Finite Groups of Order p2q2

A Simple Classification of Finite Groups of Order p2q2

... All finite groups can be broken down into a series of finite simple groups which have been called the building blocks of finite ...of finite simple groups ...

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On subgroups of finite exponent in groups

On subgroups of finite exponent in groups

... is proper in G, then G is called non-perfect, and is called perfect otherwise. Recall that a group with the maximal condition on subgroups is called Noetherian. An infinite group with all proper quotients to be ...

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Invariants of finite solvable groups

Invariants of finite solvable groups

... Bicyclic group G = AB is supersolvable, the derived subgroup of G is abelian and A contains non-identity normal subgroup in G for |A| ≥ |B| ([4], Theorems VI.4.4 and VI.10.1). From definition of bicyclic group follows ...

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Cohomologies of finite abelian groups

Cohomologies of finite abelian groups

... In this section G denotes a finite group, R = ZG. Recall that a G- lattice (or an integral representation of G) is a G-module M such that its abelian group is free of finite rank. They also say that M is a ...

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Algorithms for polycyclic by finite groups

Algorithms for polycyclic by finite groups

... The operation of the extended Schreier–Sims algorithm is based on the fol- lowing lemma, whose proof is a straightforward induction on the base length. Lemma 4.2. Let E be a polycyclic-by-finite group, H ď E and ...

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Character expansiveness in finite groups

Character expansiveness in finite groups

... a finite group usually consists of many conjugacy classes. In [8] a finite group G was called (conjugacy) expansive if for any normal subset S and any conjugacy class C of G the normal set SC consists of at ...

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On some invariants of finite groups

On some invariants of finite groups

... Proposition 2.11 ([12], Proposition 4.4). Let G be a group with the basis property. Then G/Φ(G) is a semidirect product constructed via the multiplication on some vector space over a finite field. Proposition ...

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On the total character of finite groups

On the total character of finite groups

... In [14], M. L. Lewis began the study of those groups G for which (G, Z (G)) is a Camina pair and, proved that such a group G must be a p-group for some prime p. The next lemma ([15, Lemma 2.1]) was proved by ...

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Algorithms for polycyclic by finite groups

Algorithms for polycyclic by finite groups

... At points in the thesis, the reader may encounter the phrase “without performing any element arithmetic in E”, where E is a polycyclic-by-finite group. This simply means that, while there exists some (possibly ...

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On a question of Külshammer for representations of finite groups in reductive groups

On a question of Külshammer for representations of finite groups in reductive groups

... This is in sharp contrast to the case when V is abelian: standard results from abelian cohomology (cf. [3, III, Prop. 10.4]) show that if V is an abelian unipotent group (e.g., a finite-dimensional vector space ...

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Symmetric generation of finite groups

Symmetric generation of finite groups

... CHAPTER TWO: SYMMETRIC REPRESENTATION OF L 2(ll) ELEMENTS Introduction ... 25[r] ...

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Factoring finite abelian groups

Factoring finite abelian groups

... of finite abelian groups it is usual to ask under what conditions one of the factors must be ...cyclic groups, the more general result holds [8] that if each factor has prime power order then one ...

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