p-幂零群的一个新刻画

New Characterization of p-Nilpotent Group

称子群H在群G中弱S-半置换的,如果G存在的一个次正规子群B,使得G=HB且H∩B≤HssG,其中HssG是包含在H中的G的最大的S-半置换子群.利用Sylow子群的极大子群的弱S-半置换性,并结合Sylow子群正规化子得到有限群成为p-幂零群的一个充分条件,推广了近来的一些结果.

A subgroup H of group G is said to be weakly S-semipermutabe in G if there exists a subnor- mal subgroup B of G such that G=HB and H∩B≤HssG ,where HssG is the maximal S-semipermutable subgroup of G contained in H. By using the weakly S-semipermutability of the maximal subgroups of the Sylow subgroup and combining the normalizer of Sylow subgroup,a sufficient condition for a finite group to be p-nilpotent is obtained and some recent results can be generalized.