Finite Groups with Minimal CSS-subgroups

A. A. Heliel, R. A. Hijazi, S. M. Al-Shammari

Abstract

Let G be a finite group. A subgroup H of G is called SS-quasinormal in G if there is a supplement B of H to G such that H permutes with every Sylow subgroup of B. A subgroup H of G is called CSS-subgroup in G if there exists a normal subgroup K of G such that G = HK and H ∩K is SS-quasinormal in G. In this paper, we investigate the influence of minimal CSS-subgroups of G on its structure. Our results improve and generalize several recent results in the literature.

Keywords

CSS-subgroup, c-normal subgroup, SS-quasinormal subgroup, p-nilpotent group, saturated formation

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