On K-ℙ-subnormal subgroups of finite groups

Abstract

A subgroup H of a group G is said to be K-ℙ-subnormal in G if H can be joined to the group by a chain of subgroups each of which is either normal in the next subgroup or of prime index in it. Properties of K-ℙ-subnormal subgroups are obtained. A class of finite groups whose Sylow p-subgroups are K-ℙ-subnormal in G for every p in a given set of primes is studied. Some products of K-ℙ-subnormal subgroups are investigated.