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

Let t be a fixed natural number. A subgroup H of a group G will be called K-Pₜ-subnormal 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.