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

چکیده مقاله

Let G be a finite group. The prime graph of G is a graph whose vertex set is the set of prime divisors of {pipe}G{pipe} and two distinct primes p and q are joined by an edge, whenever G contains an element of order pq. 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). © 2012 Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic.