Finite Groups with Certain Permutability Criteria

Rola A. Hijazi, Fatme M. Charaf

Abstract

Let G be a finite group. A subgroup H of G is said to be S-permutable in G if it
permutes with all Sylow subgroups of G. In this note we prove that if P, the Sylow
p-subgroup of G (p > 2), has a subgroup D such that 1 <|D|<|P| and all subgroups H of P with |H| = |D| are S-permutable in G, then G′ is p-nilpotent.

Keywords

S-Permutable Subgroup, p-Nilpotent Group, Solvable Group, Supersolvable Group.

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