Finite Groups with Minimal CSS-subgroups

  • A. A. Heliel Department of Mathematics, Faculty of Science 80203, King Abdulaziz University, Jeddah 21589, Saudi Arabia https://orcid.org/0000-0002-3425-2818
  • R. A. Hijazi Department of Mathematics, Faculty of Science 80203, King Abdulaziz University, Jeddah 21589, Saudi Arabia
  • S. M. Al-Shammari Department of Mathematics, Faculty of Science 80203, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Keywords: CSS-subgroup, c-normal subgroup, SS-quasinormal subgroup, p-nilpotent group, saturated formation

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.
Published
2021-08-05
Section
Nonlinear Analysis