scholarly journals SOME REMARKS ON THE PROBABILITY OF GENERATING AN ALMOST SIMPLE GROUP

2003 ◽  
Vol 45 (2) ◽  
pp. 281-291 ◽  
Author(s):  
FRANCESCA DALLA VOLTA ◽  
ANDREA LUCCHINI ◽  
FIORENZA MORINI
Keyword(s):  
Simple Group ◽  
Almost Simple Group

Non-commuting graphs of certain almost simple groups

2019 ◽  
Vol 12 (05) ◽  
pp. 1950081
Author(s):  
M. Jahandideh ◽  
R. Modabernia ◽  
S. Shokrolahi
Keyword(s):  
Finite Group ◽  
Abelian Group ◽  
Simple Group ◽  
Simple Groups ◽  
Almost Simple Group ◽  
Almost Simple Groups ◽  
Commuting Graph ◽  
Vertex Set

Let [Formula: see text] be a non-abelian finite group and [Formula: see text] be the center of [Formula: see text]. The non-commuting graph, [Formula: see text], associated to [Formula: see text] is the graph whose vertex set is [Formula: see text] and two distinct vertices [Formula: see text] are adjacent if and only if [Formula: see text]. We conjecture that if [Formula: see text] is an almost simple group and [Formula: see text] is a non-abelian finite group such that [Formula: see text], then [Formula: see text]. Among other results, we prove that if [Formula: see text] is a certain almost simple group and [Formula: see text] is a non-abelian group with isomorphic non-commuting graphs, then [Formula: see text].

scholarly journals COEFFICIENTS OF THE PROBABILISTIC FUNCTION OF A MONOLITHIC GROUP

2008 ◽  
Vol 50 (1) ◽  
pp. 75-81 ◽  
Author(s):  
PAZ JIMÉNEZ–SERAL
Keyword(s):  
Zeta Function ◽  
Simple Group ◽  
Almost Simple Group ◽  
Monolithic Group ◽  
Probabilistic Function

AbstractWe relate the coefficients of the probabilistic zeta function of a finite monolithic group to those of an almost simple group.

ANATOMY OF THE MONSTER: II

2002 ◽  
Vol 84 (3) ◽  
pp. 581-598 ◽  
Author(s):  
SIMON P. NORTON ◽  
ROBERT A. WILSON
Keyword(s):  
Maximal Subgroup ◽  
Simple Group ◽  
Subject Classification ◽  
Sporadic Simple Group ◽  
Almost Simple Group ◽  
Isomorphism Classes ◽  
Current State ◽  
Subgroup Problem

We describe the current state of progress on the maximal subgroup problem for the Monster sporadic simple group. Any unknown maximal subgroup is an almost simple group whose socle is in one of 19 specified isomorphism classes.2000 Mathematical Subject Classification:20D08.

scholarly journals GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST SIMPLE GROUPS

2020 ◽  
Vol 8 ◽  
Author(s):  
ANDREA LUCCHINI ◽  
CLAUDE MARION ◽  
GARETH TRACEY
Keyword(s):  
Finite Group ◽  
Maximal Subgroup ◽  
Simple Group ◽  
Finite Groups ◽  
Upper Bounds ◽  
Maximal Subgroups ◽  
Simple Groups ◽  
Almost Simple Group ◽  
Almost Simple Groups ◽  
A Finite Group

For a finite group $G$ , let $d(G)$ denote the minimal number of elements required to generate $G$ . In this paper, we prove sharp upper bounds on $d(H)$ whenever $H$ is a maximal subgroup of a finite almost simple group. In particular, we show that $d(H)\leqslant 5$ and that $d(H)\geqslant 4$ if and only if $H$ occurs in a known list. This improves a result of Burness, Liebeck and Shalev. The method involves the theory of crowns in finite groups.

RECOGNITION OF THE PROJECTIVE GENERAL LINEAR GROUP PGL(2, q) BY ITS NONCOMMUTING GRAPH

2011 ◽  
Vol 10 (02) ◽  
pp. 201-218 ◽  
Author(s):  
LIANGCAI ZHANG ◽  
WUJIE SHI
Keyword(s):  
Simple Group ◽  
Linear Group ◽  
General Linear Group ◽  
Simple Groups ◽  
General Linear ◽  
Almost Simple Group ◽  
Almost Simple Groups ◽  
Vertex Set ◽  
Noncommuting Graph ◽  
Projective General Linear Group

The noncommuting graph ∇(G) of a non-abelian group G is defined as follows. The vertex set of ∇(G) is G\Z(G) where Z(G) denotes the center of G and two vertices x and y are adjacent if and only if xy ≠ yx. It has been conjectured that if P is a finite non-abelian simple group and G is a group such that ∇(P) ≅ ∇(G), then G ≅ P. In the present paper, our aim is to consider this conjecture in the case of finite almost simple groups. In fact, we characterize the projective general linear group PGL (2, q) (q is a prime power), which is also an almost simple group, by its noncommuting graph.

scholarly journals Generalised Polygons Admitting a Point-Primitive Almost Simple Group of Suzuki or Ree Type

10.37236/5510 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Luke Morgan ◽  
Tomasz Popiel
Keyword(s):  
Normal Subgroup ◽  
Recent Result ◽  
Simple Group ◽  
Collineation Group ◽  
Minimal Normal Subgroup ◽  
Almost Simple Group ◽  
Suzuki Group ◽  
Ree Group ◽  
Point Line

Let $G$ be a collineation group of a thick finite generalised hexagon or generalised octagon $\Gamma$. If $G$ acts primitively on the points of $\Gamma$, then a recent result of Bamberg et al. shows that $G$ must be an almost simple group of Lie type. We show that, furthermore, the minimal normal subgroup $S$ of $G$ cannot be a Suzuki group or a Ree group of type $^2\mathrm{G}_2$, and that if $S$ is a Ree group of type $^2\mathrm{F}_4$, then $\Gamma$ is (up to point-line duality) the classical Ree-Tits generalised octagon.

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