关于有限群的类保持自同构的一个注记

设G是一个有限阿贝尔群A和一个阶为2n的二面体群D的半直积,其中D的每个元素通过把A的任意元映成这个元的某个幂而作用在A上。如果G的一个Sylow 2-子群有一个指数为2的阿贝尔子群,那么Out_c(G)=1。特别地,这样的有限群G具有正规化子性质。

A note on class-preserving automorphisms of finite groups

Let G be a semidirect product of a finite abelian group A and a dihedral group D of order 2n, where each element of D acts on A by raising every element of A to some fixed power. Suppose that a Sylow 2-subgroup of G has an abelian subgroup of index 2. Then Out_c(G)=1. In particular, the normalizer property holds for such a group G.