On K-Pt-subnormal subgroups of finite groups and related formations

Abstract

Let t be a fixed natural number. A subgroup H of a group G will be called K-Ptsubnormal in G if there exists a chain of subgroups H = H0 ≤ H1 ≤ · · · ≤ Hm−1 ≤ Hm = G such that either Hi−1 is normal in Hi or |Hi : Hi−1| is a some prime p and p − 1 is not divisible by the (t + 1)th powers of primes for every i = 1, . . . , n. In this work, properties of K-Pt-subnormal subgroups and classes of groups with Sylow K-Pt-subnormal subgroups are obtained.