Paper “Triple Factorizations and Supersolubility of Finite Groups” published on Proc. Edinb. Math. Soc.

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Adolfo Ballester-Bolinches and Luis M. Ezquerro.

Triple factorizations and supersolubility of finite groups.

Proc. Edinb. Math. Soc. (2), 59(2):301–309, 2016.

https://doi.org/10.1017/S0013091515000231

Abstract

In this paper we analyse the structure of a finite group of minimal order among the finite non-supersoluble groups possessing a triple factorization by supersoluble subgroups of pairwise relatively prime indices. As an application we obtain some sufficient conditions for a triple factorized group by supersoluble subgroups of pairwise relatively prime indices to be supersoluble. Many results appear as consequences of our analysis.

Keywords: Finite group, Supersoluble group, Factorization

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.