Displaying similar documents to “Arithmetical characterizations of divisor class groups. II.”

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 ) .