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THE INFLUENCE OF WEAKLY CLOSED SUBGROUPS ON THE SUPERSOLVABILITY OF A FINITE GROUP
Keywords:
weakly closed subgroup, minimal subgroup, supersolvable, saturated formationDOI:
https://doi.org/10.17654/0972555522015Abstract
Let $Z$ and $K$ be subgroups of a finite group $G$ and $Z \leq K$, if $Z^g \leq K$ for some $g \in G$ implies that $Z^g=Z$, then $Z$ is called weakly closed in $K$ (respect to $G$ ). In this paper, we investigate the supersolvabilities of a finite group $G$ by assuming that some minimal subgroups and cyclic subgroups of order 4 satisfy the weakly closed properties. Some conclusions about group formations are also obtained.
Received: February 27, 2022
Accepted: March 22, 2022
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