循环子群具有小的自同构导子的有限群

设G是有限群,H是G的子群.AutG(H)=NG(H)/CG(H)称为H在G中的自同构导子,σ(H)表示H的内自同构群.如果AutG(H)=σ(H),则称H的自同构导子是小的.若G的每个循环子群的自同构导子是小的,则称G是一个CNC-群,CNC-群的结构性质被刻画.

Finite groups with small automizers of their cyclic subgroups

Let G be a finite group and H be a subgroup of G. Aut G( H) =NG( H)/CG( H)is called automizer of H in G.σ( H) denotes the inner group of automisophism of H. The automizer of H is called small if AutG( H) = σ( H). A group G is said to be CNC- group if the automizers of all cyclic subgroups of G are small. The CNC- groups are described.