非极大交换子群皆正规的有限群

Finite groups with every non-maximal abelian subgroup being normal

设H是有限群G的一个交换子群.如果H在G中的中心化子正是它本身,则称H为G的极大交换子群.本文主要研究每一非极大交换子群都正规的有限群的结构,对这类有限群给出其完全分类.

An abelian subgroup H of a finite group G is said to be a maximal abelian subgroup in G if its centralizer is just itself. Finite groups in which every non-maximal abelian subgroup is normal are investigated, and then the classifica- tion of this kind groups is given in this paper.