A new characterization of the sporadic simple groups

Group Theory ◽  
1989 ◽  
pp. 531-540 ◽  
Keyword(s):  
Simple Groups ◽  
Sporadic Simple Groups

A NEW CHARACTERIZATION OF ALMOST SPORADIC GROUPS

2002 ◽  
Vol 01 (03) ◽  
pp. 267-279 ◽  
Author(s):  
AMIR KHOSRAVI ◽  
BEHROOZ KHOSRAVI
Keyword(s):  
Finite Group ◽  
Prime Graph ◽  
Simple Groups ◽  
Sporadic Groups ◽  
Sporadic Simple Groups ◽  
A Finite Group ◽  
Order Components ◽  
Positive Integers ◽  
Coprime Positive Integers

Let G be a finite group. Based on the prime graph of G, the order of G can be divided into a product of coprime positive integers. These integers are called order components of G and the set of order components is denoted by OC(G). Some non-abelian simple groups are known to be uniquely determined by their order components. In this paper we prove that almost sporadic simple groups, except Aut (J2) and Aut (McL), and the automorphism group of PSL(2, 2n) where n=2sare also uniquely determined by their order components. Also we discuss about the characterizability of Aut (PSL(2, q)). As corollaries of these results, we generalize a conjecture of J. G. Thompson and another conjecture of W. Shi and J. Bi for the groups under consideration.

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).

Characterization of automorphism groups of sporadic simple groups

2012 ◽  
Vol 7 (3) ◽  
pp. 513-519 ◽  
Author(s):  
Hong Shen ◽  
Hongping Cao ◽  
Guiyun Chen
Keyword(s):  
Automorphism Groups ◽  
Simple Groups ◽  
Sporadic Simple Groups

A CHARACTERIZATION OF SPORADIC SIMPLE GROUPS BY NSE AND ORDER

2012 ◽  
Vol 12 (02) ◽  
pp. 1250158 ◽  
Author(s):  
ALIREZA KHALILI ASBOEI ◽  
SEYED SADEGH SALEHI AMIRI ◽  
ALI IRANMANESH ◽  
ABOLFAZL TEHRANIAN
Keyword(s):  
Finite Group ◽  
Simple Group ◽  
Simple Groups ◽  
Sporadic Simple Group ◽  
Sporadic Simple Groups ◽  
A Finite Group

Let G be a finite group and nse (G) the set of numbers of elements with the same order in G. In this paper, we prove that if ∣G∣ = ∣S∣ and nse (G) = nse (S), where S is a sporadic simple group, then the finite group G is isomorphic to S.

scholarly journals Commuting involution graphs for sporadic simple groups

2007 ◽  
Vol 316 (2) ◽  
pp. 849-868 ◽  
Author(s):  
C. Bates ◽  
D. Bundy ◽  
S. Hart ◽  
P. Rowley
Keyword(s):  
Simple Groups ◽  
Sporadic Simple Groups

A new characterization of some finite simple groups

2015 ◽  
Vol 56 (1) ◽  
pp. 78-82 ◽  
Author(s):  
M. F. Ghasemabadi ◽  
A. Iranmanesh ◽  
F. Mavadatpour
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups

scholarly journals On the Structure of Integral Group Rings of Sporadic Groups

2000 ◽  
Vol 3 ◽  
pp. 274-306 ◽  
Author(s):  
Frauke M. Bleher ◽  
Wolfgang Kimmerle
Keyword(s):  
Automorphism Groups ◽  
Symmetric Groups ◽  
Computational Procedure ◽  
Isomorphism Problem ◽  
Simple Groups ◽  
Group Rings ◽  
Integral Group ◽  
Sporadic Groups ◽  
Integral Group Rings ◽  
Sporadic Simple Groups

AbstractThe object of this article is to examine a conjecture of Zassenhaus and certain variations of it for integral group rings of sporadic groups. We prove the ℚ-variation and the Sylow variation for all sporadic groups and their automorphism groups. The Zassenhaus conjecture is established for eighteen of the sporadic simple groups, and for all automorphism groups of sporadic simple groups G which are different from G. The proofs are given with the aid of the GAP computer algebra program by applying a computational procedure to the ordinary and modular character tables of the groups. It is also shown that the isomorphism problem of integral group rings has a positive answer for certain almost simple groups, in particular for the double covers of the symmetric groups.

scholarly journals Pointed Hopf algebras over the sporadic simple groups

2011 ◽  
Vol 325 (1) ◽  
pp. 305-320 ◽  
Author(s):  
N. Andruskiewitsch ◽  
F. Fantino ◽  
M. Graña ◽  
L. Vendramin
Keyword(s):  
Hopf Algebras ◽  
Simple Groups ◽  
Pointed Hopf Algebras ◽  
Sporadic Simple Groups
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