On the residual of a factorized group with widely supersoluble factors

摘要

Let P be the set of all primes. A subgroup H of G is called P-subnormal in G, if either H = G, or there exists a chain H = H-0 <= H-1 <= ... <= H-n = G, vertical bar H-i: Hi-1 vertical bar is an element of P, for all i: Recall that G is w-supersoluble, if every Sylow subgroup of G is P-subnormal in G. The structure of w-supersoluble residual of G = AB with P-subnormal w-supersoluble subgroups A and B is obtained.