On the unrecognizability by prime graph for the almost simple group PGL(2,9)

2016 ◽  
Vol 36 (2) ◽  
pp. 223
Author(s):  
Ali Mahmoudifar
Keyword(s):  
Simple Group ◽  
Prime Graph ◽  
Almost Simple Group

scholarly journals On the prime graph question for almost simple groups with an alternating socle

2017 ◽  
Vol 27 (03) ◽  
pp. 333-347 ◽  
Author(s):  
Andreas Bächle ◽  
Mauricio Caicedo
Keyword(s):  
Simple Group ◽  
Group Ring ◽  
Prime Graph ◽  
Integral Group Ring ◽  
Simple Groups ◽  
Alternating Group ◽  
Integral Group ◽  
Almost Simple Group ◽  
Almost Simple Groups

Let [Formula: see text] be an almost simple group with socle [Formula: see text], the alternating group of degree [Formula: see text]. We prove that there is a unit of order [Formula: see text] in the integral group ring of [Formula: see text] if and only if there is an element of that order in [Formula: see text] provided [Formula: see text] and [Formula: see text] are primes greater than [Formula: see text]. We combine this with some explicit computations to verify the prime graph question for all almost simple groups with socle [Formula: see text] if [Formula: see text].

scholarly journals Groups with the Same Prime Graph as the Simple Group D n (5)

2014 ◽  
Vol 66 (5) ◽  
pp. 666-677
Author(s):  
A. Babai ◽  
B. Khosravi
Keyword(s):  
Simple Group ◽  
Prime Graph ◽  
Group D

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].

n-RECOGNITION BY PRIME GRAPH OF THE SIMPLE GROUP PSL(2,q)

2008 ◽  
Vol 07 (06) ◽  
pp. 735-748 ◽  
Author(s):  
BEHROOZ KHOSRAVI
Keyword(s):  
Finite Group ◽  
Simple Group ◽  
Prime Number ◽  
Finite Groups ◽  
Prime Graph ◽  
Split Extension ◽  
A Finite Group

Let G be a finite group. The prime graph Γ(G) of G is defined as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p, q are joined by an edge if there is an element in G of order pq. It is proved that if p > 11 and p ≢ 1 (mod 12), then PSL(2,p) is uniquely determined by its prime graph. Also it is proved that if p > 7 is a prime number and Γ(G) = Γ(PSL(2,p2)), then G ≅ PSL(2,p2) or G ≅ PSL(2,p2).2, the non-split extension of PSL(2,p2) by ℤ2. In this paper as the main result we determine finite groups G such that Γ(G) = Γ(PSL(2,q)), where q = pk. As a consequence of our results we prove that if q = pk, k > 1 is odd and p is an odd prime number, then PSL(2,q) is uniquely determined by its prime graph and so these groups are characterizable by their prime graph.

On a conjecture about the quasirecognition by prime graph of some finite simple groups

2019 ◽  
Vol 18 (04) ◽  
pp. 1950070
Author(s):  
Ali Mahmoudifar
Keyword(s):  
Computer Program ◽  
Natural Number ◽  
Simple Group ◽  
Prime Number ◽  
Prime Power ◽  
Prime Graph ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Number Formula ◽  
Finite Linear

It is proved that some finite simple groups are quasirecognizable by prime graph. In [A. Mahmoudifar and B. Khosravi, On quasirecognition by prime graph of the simple groups [Formula: see text] and [Formula: see text], J. Algebra Appl. 14(1) (2015) 12pp], the authors proved that if [Formula: see text] is a prime number and [Formula: see text], then there exists a natural number [Formula: see text] such that for all [Formula: see text], the simple group [Formula: see text] (where [Formula: see text] is a linear or unitary simple group) is quasirecognizable by prime graph. Also[Formula: see text] in that paper[Formula: see text] the author posed the following conjecture: Conjecture. For every prime power [Formula: see text] there exists a natural number [Formula: see text] such that for all [Formula: see text] the simple group [Formula: see text] is quasirecognizable by prime graph. In this paper [Formula: see text] as the main theorem we prove that if [Formula: see text] is a prime power and satisfies some especial conditions [Formula: see text] then there exists a number [Formula: see text] associated to [Formula: see text] such that for all [Formula: see text] the finite linear simple group [Formula: see text] is quasirecognizable by prime graph. Finally [Formula: see text] by a calculation via a computer program [Formula: see text] we conclude that the above conjecture is valid for the simple group [Formula: see text] where [Formula: see text] [Formula: see text] is an odd number and [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.

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