Abstract
Let G be a finite group and H, K two nontrivial subgroups of G. We say that G is a mutually m-permutable product of H and K if G = HK and every maximal subgroup of H permutes with K and every maximal subgroup of K permutes with H. We prove the following result: Let G = G 1 G 2…G r be a finite group such that G 1, G 2,…G r are pairwise permutable subgroups of G and G i G j is a mutually m-permutable product for all i and j with i ≠ j. If the Sylow subgroups of all G i are cyclic, then G is supersolvable.
Notes
Communicated by M. Dixon.