Sylow子群皆半正规的有限群

FINITE GROUPS WITH EVERY SYLOW SUBGROUP SEMI-NORMAL

本文讨论了每个Ｓｙｌｏｗ子群均为半正规子群的有限群和每个子群均为半正规子群的有限群，给出了这两类群的若干刻划，还证明了下面两个结论：（ｌ）若Ｇ＝ＡＢ，且Ａ与Ｂ的每个Ｓｙｌｏｗ子群在Ｇ中半正规，则Ｇ为超可解群；（２）Ｇ为超可解群，当且仅当有Ｎ Ｇ，Ｇ／Ｎ为超可解群，且Ｎ的每Ｓｙｌｏｗ子群的所有极大子群在Ｇ中Ｓ－半正规。

In this paper, we investigate the finite groups whose every Sylow subgroup is semi-normal whose every subgroup is semi-normal, and provide many characterizations for these two classes of finite groups, we also prove else the following two conclusions: Ⅰ. If G=AB, and if all Sylow subgroups of A and B are semi-normal in G, then G is a supersolvable group. Ⅱ. G is a supersolvable group if and only if there exists a normal subgroup N of G such that G/N is a supersol-vable group and all maximal subgroups of every Sylow subgroup of H are S-seminormal in G.