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On small distances of small 2-groups

Natalia Zhukavets (2001)

Commentationes Mathematicae Universitatis Carolinae

The paper reports the results of a search for pairs of groups of order n that can be placed in the distance n 2 / 4 for the case when n { 16 , 32 } . The constructions that are used are of the general character and some of their properties are discussed as well.

On sM-group.

How, Guan Aun (2003)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

On the composition factors of a group with the same prime graph as B n ( 5 )

Azam Babai, Behrooz Khosravi (2012)

Czechoslovak Mathematical Journal

Let G be a finite group. The prime graph of G is a graph whose vertex set is the set of prime divisors of | G | and two distinct primes p and q are joined by an edge, whenever G contains an element of order p q . The prime graph of G is denoted by Γ ( G ) . It is proved that some finite groups are uniquely determined by their prime graph. In this paper, we show that if G is a finite group such that Γ ( G ) = Γ ( B n ( 5 ) ) , where n 6 , then G has a unique nonabelian composition factor isomorphic to B n ( 5 ) or C n ( 5 ) .

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