scholarly journals Vertex-primitive s-arc-transitive digraphs of alternating and symmetric groups

2020 ◽  
Vol 544 ◽  
pp. 75-91
Author(s):  
Jiangmin Pan ◽  
Cixuan Wu ◽  
Fugang Yin
Keyword(s):  
Symmetric Groups ◽  
Alternating And Symmetric Groups ◽  
Vertex Primitive

The factorisation of the alternating and symmetric groups

1980 ◽  
Vol 175 (2) ◽  
pp. 171-179 ◽  
Author(s):  
James Wiegold ◽  
Alan G. Williamson
Keyword(s):  
Symmetric Groups ◽  
Alternating And Symmetric Groups

scholarly journals On alternating and symmetric groups which are quasi OD-characterizable

2017 ◽  
Vol 16 (04) ◽  
pp. 1750065 ◽  
Author(s):  
Ali Reza Moghaddamfar
Keyword(s):  
Finite Group ◽  
Symmetric Group ◽  
Prime Graph ◽  
Symmetric Groups ◽  
Degree Pattern ◽  
Alternating And Symmetric Groups ◽  
A Finite Group

Let [Formula: see text] be the prime graph associated with a finite group [Formula: see text] and [Formula: see text] be the degree pattern of [Formula: see text]. A finite group [Formula: see text] is said to be [Formula: see text]-fold [Formula: see text]-characterizable if there exist exactly [Formula: see text] nonisomorphic groups [Formula: see text] such that [Formula: see text] and [Formula: see text]. The purpose of this paper is two-fold. First, it shows that the symmetric group [Formula: see text] is [Formula: see text]-fold [Formula: see text]-charaterizable. Second, it shows that there exist many infinite families of alternating and symmetric groups, [Formula: see text] and [Formula: see text], which are [Formula: see text]-fold [Formula: see text]-characterizable with [Formula: see text].

Quasi-permutation representations of alternating and symmetric groups*

2007 ◽  
Vol 27 (2) ◽  
pp. 297-300
Author(s):  
Behravesh Houshang ◽  
Hossein Jafari Mohammad
Keyword(s):  
Symmetric Groups ◽  
Alternating And Symmetric Groups

scholarly journals Lower signalizer lattices in alternating and symmetric groups

2012 ◽  
Vol 15 (2) ◽  
Author(s):  
Michael Aschbacher
Keyword(s):  
Symmetric Groups ◽  
Subgroup Lattices ◽  
Alternating And Symmetric Groups

Abstract.We prove that the subgroup lattices of finite alternating and symmetric groups do not contain so-called lower signalizer lattices in the class

A Geometrical Study of the Alternating and Symmetric Groups

1929 ◽  
Vol 25 (2) ◽  
pp. 168-174 ◽  
Author(s):  
G. de B. Robinson
Keyword(s):  
Finite Group ◽  
Hermitian Form ◽  
Symmetric Groups ◽  
Irreducible Group ◽  
Image Position ◽  
Alternating And Symmetric Groups ◽  
A Finite Group

Let a finite group Τ be represented as an irreducible group of order N of linear substitutions on n variables,The variables may be chosen so that the substitutions of the group leave invariant the Hermitian form

scholarly journals Generators for Alternating and Symmetric Groups

1971 ◽  
Vol 12 (1) ◽  
pp. 63-68 ◽  
Author(s):  
I. M. S. Dey ◽  
James Wiegold
Keyword(s):  
Free Product ◽  
Modular Group ◽  
Symmetric Groups ◽  
Alternating Groups ◽  
Generating Set ◽  
Alternating And Symmetric Groups

Let Γ denote the modular group, that is, the free product of a group of order 2 and a group of order 3. Morris Newman investigates in [2] the factor-groups of Γ and calls them Γ-groups for short; thus a group is a Γ-group if and only if it has a generating set consisting of an element of order dividing 2 and an element of order dividing 3. Newman's interest centres on finite simple Γ-groups. He proves that the linear fractional groups LF(2,p) for primes p are Γ -groups, and poses the problem of deciding which of the alternating groups enjoy this property.

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