Paper “On mutually permutable products of finite groups” published in Rend. Lincei. Mat. Appl.

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Adolfo Ballester-Bolinches, Yangming Li, Mari Carmen Pedraza-Aguilera.

On mutually permutable products of finite groups

Rend. Lincei. Mat. Appl., 29 (4):711-719, 2018

doi:10.4171/RLM/830

Abstract

The main purpose of this paper is to study mutually permutable products G=AB in which the subgroups of prime order p and cyclic of order 4 (if p=2) of the largest normal subgroup of G contained in A \cap B are well situated in G. Our results confirm once again the important role of the intersection of the factors in the structural study of mutually permutable products.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite group, Sylow permutability, weakly s-supplementation, factorisation, saturated formation.

Paper “Prefactorized subgroups in pairwise mutually permutable products” published in Ann. Mat. Pura Appl.

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A. Ballester-Bolinches, J. C. Beidleman, H. Heineken, M. C. Pedraza-Aguilera

Prefactorized subgroups in pairwise mutually permutable subgroups

Ann. Math .Pura Appl., 192(6), 1043-1057 (2013)

http://dx.doi.org/10.1007/s10231-012-0257-y

Abstract

We continue here our study of pairwise mutually and pairwise totally permutable products. We are looking for subgroups of the product in which the given factorization induces a factorization of the subgroup. In the case of soluble groups, it is shown that a prefactorized Carter subgroup and a prefactorized system normalizer exist. A less stringent property have F-residual, F-projector and F-normalizer for any saturated formation F including the supersoluble groups.

MSC: 20D10, 20D20

Keywords: Finite group, Permutability, Factorization, Saturated formation.

Paper “On a problem of L.A. Shemetkov on superradical formations of finite groups” published in J. Algebra

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A. Ballester-Bolinches, S. F. Kamornikov, V. N. Tyutyanov

On a problem of L.A. Shemetkov on superradical formations of finite groups

J. Algebra, 403, 69-76 (2014)

http://dx.doi.org/10.1016/j.jalgebra.2014.01.004

Abstract: Subgroup-closed saturated formations F which are closed under taking products of F-subnormal F-subgroups are studied in the paper. Our results can be regarded as further developments in the hunt for a solution of a problem proposed by L.A. Shemetkov in 1999 in the Kourovka Notebook.

MSC: 20D10, 20D20
Keywords: Finite group, saturated formation, critical group