@article{Heliel2023, 
author = {A. A. Heliel and A. Ballester-Bolinches and M. M. Al-Shomrani and R. A. Al-Obidy},
title = {On    σ-subnormal subgroups and products of finite groups},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {2},
pages = {770-775},
keywords = {finite group, σ-soluble group, σ-subnormal subgroup, products of groups},
url = {https://www.sciopen.com/article/10.3934/era.2023038},
doi = {10.3934/era.2023038},
abstract = {Suppose that    σ  =  {            σ              i        :  i  ∈  I  } is a partition of the set        P   of all primes. A subgroup    A of a finite group    G is said to be    σ-subnormal in    G if    A can be joined to    G by a chain of subgroups    A  =      A          0        ⊆      A          1        ⊆  ⋯  ⊆      A          n        =  G such that either        A          i      −      1       normal in        A          i       or        A          i            /    C  o  r      e                  A                  i                      (      A          i      −      1        ) is a              σ              j      -group for some    j  ∈  I, for every    1  ≤  i  ≤  n. A    σ-subnormality criterion related to products of subgroups of finite    σ-soluble groups is proved in the paper. As a consequence, a characterisation of the    σ-Fitting subgroup of a finite    σ-soluble group naturally emerges.}
}