scholarly journals Flag-Transitive Point-Primitive Symmetric $(v,k,\lambda)$ Designs with Large $k$

10.37236/9335 ◽  
2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Zhilin Zhang ◽  
Pingzhi Yuan ◽  
Shenglin Zhou
Keyword(s):  
Automorphism Group ◽  
Simple Group ◽  
Almost Simple Group ◽  
Transitive Point

In 2012, Tian and Zhou conjectured that a flag-transitive and point-primitive automorphism group of a symmetric $(v,k,\lambda)$ design must be an affine or almost simple group. In this paper, we study this conjecture and prove that if $k\leqslant 10^3$ and $G\leqslant Aut(\mathcal{D})$ is flag-transitive, point-primitive, then $G$ is affine or almost simple. This support the conjecture.

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].

NATURAL EXISTENCE PROOF FOR LYONS SIMPLE GROUP

2003 ◽  
Vol 02 (03) ◽  
pp. 277-315
Author(s):  
GERHARD O. MICHLER ◽  
MICHAEL WELLER ◽  
KATSUSHI WAKI
Keyword(s):  
Automorphism Group ◽  
Simple Group ◽  
Conjugacy Classes ◽  
Existence Proof ◽  
Sporadic Simple Group ◽  
Character Tables ◽  
The Given ◽  
Fold Cover

In this article we give a self-contained existence proof for Lyons' sporadic simple group G by application of the first author's algorithm [18] to the given centralizer H ≅ 2A11 of a 2-central involution of G. It also yields four matrix generators of G inside GL 111 (5) which are given in Appendix A. From the subgroup U ≅ (3 × 2A8) : 2 of H ≅ 2A11, we construct a subgroup E of G which is isomorphic to the 3-fold cover 3McL: 2 of the automorphism group of the McLaughlin group McL. Furthermore, the character tables of E ≅ 3McL : 2 and G are determined and representatives of their conjugacy classes are given as short words in their generating matrices.

Quasirecognition of E6(q) by the orders of maximal abelian subgroups

2018 ◽  
Vol 17 (07) ◽  
pp. 1850122 ◽  
Author(s):  
Zahra Momen ◽  
Behrooz Khosravi
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Simple Group ◽  
Outer Automorphism ◽  
Composition Factor ◽  
Outer Automorphism Group ◽  
Abelian Subgroups ◽  
A Finite Group ◽  
Nonabelian Composition Factor

In [Li and Chen, A new characterization of the simple group [Formula: see text], Sib. Math. J. 53(2) (2012) 213–247.], it is proved that the simple group [Formula: see text] is uniquely determined by the set of orders of its maximal abelian subgroups. Also in [Momen and Khosravi, Groups with the same orders of maximal abelian subgroups as [Formula: see text], Monatsh. Math. 174 (2013) 285–303], the authors proved that if [Formula: see text], where [Formula: see text] is not a Mersenne prime, then every finite group with the same orders of maximal abelian subgroups as [Formula: see text], is isomorphic to [Formula: see text] or an extension of [Formula: see text] by a subgroup of the outer automorphism group of [Formula: see text]. In this paper, we prove that if [Formula: see text] is a finite group with the same orders of maximal abelian subgroups as [Formula: see text], then [Formula: see text] has a unique nonabelian composition factor which is isomorphic to [Formula: see text].

scholarly journals No sporadic almost simple group acts primitively on the points of a generalised quadrangle

2021 ◽  
Vol 344 (4) ◽  
pp. 112291
Author(s):  
John Bamberg ◽  
James Evans
Keyword(s):  
Simple Group ◽  
Almost Simple Group ◽  
Generalised Quadrangle

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.

scholarly journals The 2-fusion system of an almost simple group

2020 ◽  
Vol 561 ◽  
pp. 5-16
Author(s):  
Michael Aschbacher
Keyword(s):  
Simple Group ◽  
Fusion System ◽  
Almost Simple Group

scholarly journals The automorphism group of the Tits simple group $\sp{2}F\sb{4}(2)\sp’ $

1975 ◽  
Vol 52 (1) ◽  
pp. 75-75
Author(s):  
Robert L. Griess ◽  
Richard Lyons
Keyword(s):  
Automorphism Group ◽  
Simple Group

AUTOMORPHISM GROUPS OF SELF-COMPLEMENTARY VERTEX-TRANSITIVE GRAPHS

2015 ◽  
Vol 93 (2) ◽  
pp. 238-247
Author(s):  
ZHAOHONG HUANG ◽  
JIANGMIN PAN ◽  
SUYUN DING ◽  
ZHE LIU
Keyword(s):  
Automorphism Group ◽  
Simple Group ◽  
Automorphism Groups ◽  
Composition Factor ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs ◽  
Free Order

Li et al. [‘On finite self-complementary metacirculants’, J. Algebraic Combin.40 (2014), 1135–1144] proved that the automorphism group of a self-complementary metacirculant is either soluble or has $\text{A}_{5}$ as the only insoluble composition factor, and gave a construction of such graphs with insoluble automorphism groups (which are the first examples of self-complementary graphs with this property). In this paper, we will prove that each simple group is a subgroup (so is a section) of the automorphism groups of infinitely many self-complementary vertex-transitive graphs. The proof involves a construction of such graphs. We will also determine all simple sections of the automorphism groups of self-complementary vertex-transitive graphs of $4$-power-free order.

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