On σ-Subnormal Subgroups of Finite Groups

Abstract

Throughout this paper, all groups are finite and σ is some partition of the set of all primes P (that is, σ = {σi | i ∈ I}, where P = ∪i∈Iσi and σi ∩ σj = ∅ for all i =6 j). A subgroup A of a group G is said to be σ-subnormal in G if there is a subgroup chain A = A0 ≤ A1 ≤ · · · ≤ An = G such that either Ai−1 E Ai or Ai/(Ai−1)Ai is a σj-group for some j = j(i) for all i = 1, . . . , n. In this review, we discuss some known results of the theory of σ-subnormal subgroups and also some open questions in this line research.