Sylow p-子群的非平凡子群与有限群的p-超可解性

Non-trivial Subgroups of Sylow p-subgroups and the p-supersolvability of Finite Groups

设E是有限群G的正规子群使得G/E为p-超可解群,P是E的正规的Sylowp-子群,其中p为一奇素数,如果P存在一个子群D满足以下性质:1<︱D︱<︱P︱,对于任意的H≤P,︱H︱=︱D︱,H在G中正规,则G为p-超可解群.

Let E be a normal subgroup of a finite group G such that G/E is p-supersolvability,P a normal Sylow p-subgroup of E,where p is an odd prime.If there exists a subgroup D of P such that 1︱D︱︱P︱ and every subgroup H of P with order ︱D︱ is normal in G,then G is p-supersolvable.