Finite Groups with Certain Permutability Criteria
DOI:
https://doi.org/10.29020/nybg.ejpam.v12i2.3399Keywords:
S-Permutable Subgroup, p-Nilpotent Group, Solvable Group, Supersolvable Group.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.
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