On the composition factors of a group with the same prime graph as B
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Authors: | Azam Babai Behrooz Khosravi |
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Institution: | 1. Dept. of Pure Math., Faculty of Math. and Computer Sci. Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran, 15914, Iran
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Abstract: | 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 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). |
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