Thompson’s conjecture for some finite simple groups with connected prime graph

2013 ◽  
Vol 51 (6) ◽  
pp. 451-478 ◽  
Author(s):  
N. Ahanjideh
Keyword(s):  
Prime Graph ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Thompson’S Conjecture

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].

Quasirecognition by prime graph of finite simple groups L n (2) and U n (2)

2010 ◽  
Vol 132 (1-2) ◽  
pp. 140-153 ◽  
Author(s):  
Behrooz Khosravi ◽  
Hossein Moradi
Keyword(s):  
Prime Graph ◽  
Simple Groups ◽  
Finite Simple Groups

A Characterization of Finite Simple Groups by the Degrees of Vertices of Their Prime Graphs

2005 ◽  
Vol 12 (03) ◽  
pp. 431-442 ◽  
Author(s):  
A. R. Moghaddamfar ◽  
A. R. Zokayi ◽  
M. R. Darafsheh
Keyword(s):  
Finite Group ◽  
Prime Graph ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Natural Numbers ◽  
Prime Graphs ◽  
Sporadic Simple Groups ◽  
A Finite Group ◽  
Groups Of Lie Type

If G is a finite group, we define its prime graph Γ(G) 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, denoted by p~q, if there is an element in G of order pq. Assume [Formula: see text] with primes p1<p2<⋯<pkand natural numbers αi. For p∈π(G), let the degree of p be deg (p)=|{q∈π(G)|q~p}|, and D(G):=( deg (p1), deg (p2),…, deg (pk)). In this paper, we prove that if G is a finite group such that D(G)=D(M) and |G|=|M|, where M is one of the following simple groups: (1) sporadic simple groups, (2) alternating groups Apwith p and p-2 primes, (3) some simple groups of Lie type, then G≅M. Moreover, we show that if G is a finite group with OC (G)={29.39.5.7, 13}, then G≅S6(3) or O7(3), and finally, we show that if G is a finite group such that |G|=29.39.5.7.13 and D(G)=(3,2,2,1,0), then G≅S6(3) or O7(3).

scholarly journals Quasirecognition by Prime Graph of the Groups 2D2n(q) Where q < 105

2017 ◽  
Author(s):  
Hossein Moradi ◽  
Mohammad Reza Darafsheh ◽  
Ali Iranmanesh
Keyword(s):  
Finite Group ◽  
Simple Group ◽  
Prime Power ◽  
Prime Graph ◽  
Composition Factor ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Prime Divisors ◽  
A Finite Group

Let G be a finite group. The prime graph &Gamma;(G) of G is defined as follows: The set of vertices of&nbsp;&Gamma;(G) is the set of prime divisors of |G| and two distinct vertices p and p' are connected in &Gamma;(G), whenever G has an element of order pp'. A non-abelian simple group P is called recognizable by prime graph if for any finite group G with &Gamma;(G)=&Gamma;(P), G has a composition factor isomorphic to P. In&nbsp;[4] proved finite simple groups 2Dn(q), where&nbsp;n&nbsp;&ne; 4k are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups 2D2k(q), where&nbsp;k &ge; 9 and q is a prime power less than 105.

OD-Characterization of the Projective Special Linear Groups L2(q)

2012 ◽  
Vol 19 (03) ◽  
pp. 509-524 ◽  
Author(s):  
Liangcai Zhang ◽  
Wujie Shi
Keyword(s):  
Prime Graph ◽  
Simple Groups ◽  
Linear Groups ◽  
Finite Simple Groups ◽  
Projective Special Linear Group ◽  
Special Linear ◽  
Projective Special Linear Groups ◽  
Special Linear Groups

Let L2(q) be the projective special linear group, where q is a prime power. In the present paper, we prove that L2(q) is OD-characterizable by using the classification of finite simple groups. A new method is introduced in order to deal with the subtle changes of the prime graph of a group in the discussion of its OD-characterization. This not only generalizes a result of Moghaddamfar, Zokayi and Darafsheh, but also gives a positive answer to a conjecture put forward by Shi.

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