科研之友
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摘要
Let G be a group and omega(G) be the set of element orders of G. Let k a omega(G) and m (k) (G) be the number of elements of order k in G. Let nse(G) = {m (k) (G): k a omega(G)}. Assume r is a prime number and let G be a group such that nse(G) = nse(S (r) ), where S (r) is the symmetric group of degree r. In this paper we prove that G ae... S (r) , if r divides the order of G and r (2) does not divide it. To get the conclusion we make use of some well-known results on the prime graphs of finite simple groups and their components.
- 出版日期2017-6
