On Nearly S-Permutable Subgroups of Finite Groups

Abstract

We say that a subgroup H of a finite group G is nearly S-permutable in G if for every prime p such that (p, |H|) = 1 and for every subgroup K of G containing H the normalizer N _K (H) contains some Sylow p-subgroup of K. We study the structure of G under the assumption that some subgroups of G are nearly S-permutable in G.

Key Words:

• Maximal subgroup
• Nearly S-permutable subgroup
• Saturated formation
• Solvable group
• Supersolvable group
• The generalized Fitting subgroup

2000 Mathematics Subject Classification:

• 20D10
• 20D15

Notes

Communicated by A. Turull.