Structure of finite groups, in which any pronormal subgroup is either normal or abnormal

A.A. Pypka (Oles Honchar Dnipropetrovsk National University),


A subgroup $$$H$$$ of a group $$$G$$$ is said to be abnormal in $$$G$$$ if, for each element $$$g \in G$$$, we have $$$g \in {<}H, H^g{>}$$$. A subgroup $$$H$$$ of a group $$$G$$$ is said to be pronormal in $$$G$$$ if, for each element $$$g \in G$$$, the subgroups $$$H$$$ and $$$H^g$$$ are conjugate in $$${<}H, H^g{>}$$$. We describe all finite groups, each pronormal subgroup in which is either normal or abnormal.


abnormal subgroup; pronormal subgroup


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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991