幂零群的若干充分条件

Some sufficient conditions of a nilpotent group

设G为有限群 ,α是G的一个对合自同构 ,若O2 (G)∈Sy|2 G且α在G/O2 (G)上诱导一个无不动点的自同构 ,那么O2 (G)在G中有α—不变的补子群H ,并且在某些条件下G是幂零群 .

Let G be a finite group with an involutorical automorphism α .If O 2(G)∈ Sy | 2(G) and α induces an fixed-point-free automorphism on G/O 2(G) ,then O 2(G) has an α -invariant complement H in G .And G will be nilpotent under some other conditions.