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ON MINIMAL $CSS$-SUBGROUPS OF FINITE GROUPS
Keywords:
S-quasinormal subgroup, SS-quasinormal subgroup, C-normal subgroup, CSS-subgroup, nilpotent group, p-nilpotent group, supersolvable group, saturated formation.DOI:
https://doi.org/10.17654/0972555525035Abstract
A subgroup $V$ of a finite group $X$ is called $C S S$-subgroup in $X$ if we can find a normal subgroup $W$ of $X$ satisfies $X=V W$ and $V \cap W$ is $S S$-quasinormal in $X$. In this paper, we use a $C S S$-subgroup condition on minimal subgroups to study the structure of the finite group $X$. Our theories improve and extend the recent and the classical results in the literature.
Received: July 27, 2025
Revised: August 31, 2025
Accepted: September 6, 2025
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