科研之友
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摘要
Suppose G is a group which is p-stable and p-constrained, where p is an odd prime, and S is a Sylow p-subgroup of G. A classical theorem of Glauberman shows that Z J (S) O-p' (G) < G, where J (S) is the Thompson subgroup of S. In this paper, we generalize the above result by replacing the odd prime p with a set pi of odd primes. More precisely, suppose pi is a set of odd primes and G is an E-pi(n) group which is pi-stable and pi-constrained. We prove that if H is an element of Hall(pi) (G), then ZJ(H)O-pi' (G) < G and G = N-G (ZJ(H))O-pi' (G). An interesting application is also given.
