$$c^*$$ c ∗ -Normal and s-semipermutable subgroups in finite groups

Abstract

A subgroup \(H\) of a group \(G\) is called \(c^*\)-normal in \(G\) if there exists a normal subgroup \(N\) of \(G\) such that \(G=HN\) and \(H\cap N\) is \(S\)-quasinormally embedded in \(G\). A subgroup \(K\) of \(G\) is said to be \(s\)-semipermutable if it is permutable with every Sylow \(p\)-subgroup of \(G\) with \((p, |K|)=1\). In this article, we investigate the influence of \(c^*\)-normality and \(s\)-semipermutability of subgroups on the structure of finite groups and generalize some known results.