Characterization of the finite simple groups by spectrum and order

2009 ◽  
Vol 48 (6) ◽  
pp. 385-409 ◽  
Author(s):  
A. V. Vasil’ev ◽  
M. A. Grechkoseeva ◽  
V. D. Mazurov
Keyword(s):  
Simple Groups ◽  
Finite 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

CHARACTERIZATION OF SOME FINITE SIMPLE GROUPS

1971 ◽  
Vol 5 (4) ◽  
pp. 805-814
Author(s):  
V A Belonogov
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups

scholarly journals A theorem on generation of finite orthogonal groups

1973 ◽  
Vol 16 (4) ◽  
pp. 495-506 ◽  
Author(s):  
W. J. Wong
Keyword(s):  
Finite Fields ◽  
Simple Groups ◽  
Symplectic Groups ◽  
Finite Simple Groups ◽  
Intermediate Result ◽  
Orthogonal Groups ◽  
Generators And Relations ◽  
Groups Of Lie Type

Presentation in terms of generators and relations for the classical finite simple groups of Lie type have been given by Steinberg and Curtis [2,4]. These presentations are useful in proving characterzation theorems for these groups, as in the author's work on the projective symplectic groups [5]. However, in some cases, the application is not quite instantaneous, and an intermediate result is needed to provide a presentation more suitable for the situation in hand. In this paper we prove such a result, for the orthogonal simple groups over finite fields of odd characteristic. In a subsequent article we shall use this to give a characterization of these groups in terms of the structure of the centralizer of an involution.

On the Mathieu group M23

1971 ◽  
Vol 12 (4) ◽  
pp. 385-392 ◽  
Author(s):  
N. Bryce
Keyword(s):  
Simple Group ◽  
Finite Simple Group ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Unique Determination ◽  
Mathieu Group ◽  
Mathieu Groups

Until 1965, when Janko [7] established the existence of his finite simple group J1, the five Mathieu groups were the only known examples of isolated finite simple groups. In 1951, R. G. Stanton [10] showed that M12 and M24 were determined uniquely by their order. Recent characterizations of M22 and M23 by Janko [8], M22 by D. Held [6], and M11 by W. J. Wong [12], have facilitated the unique determination of the three remaining Mathieu groups by their orders. D. Parrott [9] has so characterized M22 and M11, while this paper is an outline of the characterization of M23 in terms of its order.

A characterization of finite simple groups by the orders of solvable subgroups

2007 ◽  
Vol 50 (5) ◽  
pp. 715-726
Author(s):  
Klaus Denecke ◽  
Xian-hua Li ◽  
Jian-xing Bi
Keyword(s):  
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).

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