ON THE DIRECT PRODUCT OF NEARLY S-PERMUTABLE SUBGROUPS

A subgroup H is said to be S-permutable in G if it permutes with all Sylow subgroups of G. A subgroup H of G is called nearly S-permutable in G if for every prime p such that gcd(p, |H|) = 1 and for every subgroup K of G containing H, the normalizer NK(H) contains some Sylow p-subgroup of K. The main aims of this article is to classify the family of all nearly S-permutable subgroups for certain groups and study the direct product of their subgroups. Moreover, we prove that the direct product of certain nearly S-permutable subgroups is necessary nearly S-permutable. ? 2022 Academic Publications