New Criteria for Quasi-$\varvec{\mathscr {F}}$-Groups

Abstract

Let G be a finite group and $\mathscr {F}$ a saturated formation of finite groups. Then G is a quasi-$\mathscr {F}$-group if for every $\mathscr {F}$-eccentric chief factor H / K of G and every $x\in G$, x induces an inner automorphism on H / K. In this article, we obtain some results about the quasi-$\mathscr {F}$-groups and use them to give the conditions under which a group is quasisupersoluble.

Keywords

$\mathscr {F}$-groups')">Quasi-$\mathscr {F}$-groups / Sylow subgroups / ${\mathcal {M}}$-supplemented subgroups')">${\mathcal {M}}$-supplemented subgroups / Solubly saturated formation

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Funding

NSFC(11701223)

NSFC(11501235)

the Key Natural Science Foundation of Anhui Education Commission(KJ2017A569)

Research project of China West Normal University(17E091)