(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Let G be a finite group. A subgroup H of G is S-permutable in G if H permutes with every Sylow subgroup of G. A subgroup H of G is called an SSH-subgroup in G if G has an S-permutable subgroup K such that H^SG =HK and H^g N_K(H) H, for all g G, where H^SG is the intersection of all S-permutable subgroups of G containing H. In this paper, we investigate the structure of a finite group G under the assumption that certain subgroups of prime power orders are SSH-subgroups of G.