Group classes and mutually permutable products

Abstract

Let G = AB be the mutually permutable product of the nontrivial subgroups A and B of the group G. Then A or B contains a nontrivial normal subgroup of G. It is also established that S(G) ∩ A = S(A), where S(U) is the solvable radical of U. These facts lead to some generalized results about mutually permutable products of SC-groups. It is also shown that if G is a PTS-group, then A and B are PST-groups. © 2005 Elsevier Inc. All rights reserved.