scholarly journals On the automorphism groups of symmetric graphs admitting an almost simple group

2008 ◽  
Vol 29 (6) ◽  
pp. 1467-1472 ◽  
Author(s):  
Xin Gui Fang ◽  
Lu Jun Jia ◽  
Jie Wang
Keyword(s):  
Simple Group ◽  
Automorphism Groups ◽  
Almost Simple Group ◽  
Symmetric Graphs

scholarly journals Almost Simple Groups of Lie Type and Symmetric Designs with $\lambda$ Prime

10.37236/9366 ◽  
2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Seyed Hassan Alavi ◽  
Mohsen Bayat ◽  
Ashraf Daneshkhah
Keyword(s):  
Projective Space ◽  
Simple Group ◽  
Finite Simple Group ◽  
Automorphism Groups ◽  
Simple Groups ◽  
Almost Simple Group ◽  
Group Of Lie Type ◽  
Symmetric Designs ◽  
Almost Simple Groups ◽  
Groups Of Lie Type

In this article, we investigate symmetric $(v,k,\lambda)$ designs $\mathcal{D}$ with $\lambda$ prime admitting flag-transitive and point-primitive automorphism groups $G$. We prove that if $G$ is an almost simple group with socle a finite simple group of Lie type, then $\mathcal{D}$ is either the point-hyperplane design of a projective space $\mathrm{PG}_{n-1}(q)$, or it is of parameters  $(7,4,2)$, $(11,5,2)$, $(11,6,3)$ or $(45,12,3)$.

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.

scholarly journals Automorphism groups of symmetric graphs of valency 3

1989 ◽  
Vol 47 (1) ◽  
pp. 60-72 ◽  
Author(s):  
Marston Conder ◽  
Peter Lorimer
Keyword(s):  
Automorphism Groups ◽  
Symmetric Graphs

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.

scholarly journals Invariant Graph Partition Comparison Measures

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 504 ◽  
Author(s):  
Fabian Ball ◽  
Andreas Geyer-Schulz
Keyword(s):  
Invariant Measures ◽  
Automorphism Groups ◽  
Structural Difference ◽  
Equivalence Classes ◽  
Classical Counterpart ◽  
Symmetric Graphs ◽  
Invariant Graph ◽  
Partition Space ◽  
Comparison Measures ◽  
Pseudometric Space

Symmetric graphs have non-trivial automorphism groups. This article starts with the proof that all partition comparison measures we have found in the literature fail on symmetric graphs, because they are not invariant with regard to the graph automorphisms. By the construction of a pseudometric space of equivalence classes of permutations and with Hausdorff’s and von Neumann’s methods of constructing invariant measures on the space of equivalence classes, we design three different families of invariant measures, and we present two types of invariance proofs. Last, but not least, we provide algorithms for computing invariant partition comparison measures as pseudometrics on the partition space. When combining an invariant partition comparison measure with its classical counterpart, the decomposition of the measure into a structural difference and a difference contributed by the group automorphism is derived.

Sign in / Sign up

Export Citation Format

Share Document