Paper «On σ-subnormal subgroups of factorised finite groups» published in J. Algebra

The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:

A. Ballester-Bolinches, S. F. Kamornikov, M. C. Pedraza-Aguilera, and X. Yi.
On σ-subnormal subgroups of factorised finite groups.
J. Algebra, 559:195–202, 2020.



Let σ = {σi : iI} be a partition of the set ℙ of all prime numbers. A subgroup X of a finite group G is called σsubnormal in G if there is chain of subgroups X = X0X1 ⊆⋯⊆ Xn = G with Xj-1 normal in Xj or Xi/CoreXi(Xi-1) is a σ-group for some iI, 1 ≤ jn. In the special case that σ is the partition of ℙ into sets containing exactly one prime each, the σ-subnormality reduces to the familiar case of subnormality.

If a finite soluble group G = AB is factorised as the product of the subgroups A and B, and X is a subgroup of G such that X is σ-subnormal in 〈X, Xg〉 for all gAB , we prove that X is σ-subnormal in G. This is an extension of a subnormality criteria due to Maier and Sidki and Casolo.

2020 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite group; Soluble group; σ-Subnormal subgroup; σ-Nilpotency; Factorised group