超可解群的两个充分条件

Two Sufficient Conditions for Supersolvability of Finite Groups

X是群G的非空子集,称G的子群H在G中X-ss-半置换的,如果H在G中有补充T,只要(p,|H|)=1就有H与T的每个Sylow p-子群是X-置换的.利用准素子群的X-ss-半置换性,给出超可解的两个充分条件.

Let X be a nonempty subset of a group G and H a subgroup of G. H is said to be X-ss- semipermutable in G if G has a supplement T such that H is X- permuable with the Sylow p-subgoup of T, where （p, ｜H｜） = 1. In this paper, by using properties of X- ss - semipermutable primary subgroups, two sufficient condi- tions are obtained under which a group is supersolvable.