On finite groups with given $ICΦ$-subgroups

Research output: Preprint/documentation/reportPreprint



A subgroup $H$ of a group $G$ is said to be an $IC\Phi$-subgroup of $G$ if $H \cap [H,G] \le \Phi(H)$. We analyze the structure of a finite group $G$ under the assumption that some given subgroups of $G$ are $IC\Phi$-subgroups of $G$. A new characterization of finite abelian groups and some new criteria for $2$-nilpotence and nilpotence of finite groups will be obtained. Moreover, we will obtain two criteria for a finite group to lie in a given solvably saturated formation containing the class of finite supersolvable groups.


Original languageEnglish
Number of pages10
Publication statusPublished - 7 Mar 2022
No renderer: customAssociatesEventsRenderPortal,dk.atira.pure.api.shared.model.researchoutput.WorkingPaper


DFG Classification of Subject Areas according to Review Boards

Subject groups, research areas, subject areas according to Destatis


  • math.GR

Library keywords