On IC Φ S – subgroups of finite groups

Let H be a subgroup of a group G. Then H is called an ICΦs− subgroup of G if (H∩[H,G])HG/HG⊆Φ(H/HG)HsG/HG, where HsG is the subgroup of H generated by all those subgroups of H which are s-permutable in G. We prove the p-supersolvability of a finite group G under the assumption that certain p-subgroups of G are ICΦs− subgroups of G. Our main result generalizes and extends some recent work of Gao and Li (2022).