On 𝑐-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups

Wei, Huaquan; Wang, Yanming; Li, Yangming

doi:10.1090/S0002-9939-04-07296-X

On $c$-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups
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by Huaquan Wei, Yanming Wang and Yangming Li PDF

Proc. Amer. Math. Soc. 132 (2004), 2197-2204 Request permission

Abstract:

This paper proves: Let $\mathcal {F}$ be a saturated formation containing $\mathcal {U}$. Suppose that $G$ is a group with a normal subgroup $H$ such that $G/H \in \mathcal {F}$. (1) If all maximal subgroups of any Sylow subgroup of $F^*(H)$ are $c$-supple- mented in $G$, then $G \in \mathcal {F}$; (2) If all minimal subgroups and all cyclic subgroups with order 4 of $F^*(H)$ are $c$-supplemented in $G$, then $G \in \mathcal {F}$.

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