Paper “Finite trifactorised groups and $\pi$-decomposability” published in Bull. Austral. Math. Soc.

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L. S. Kazarin, A. Martínez-Pastor, M. D. Pérez-Ramos.

Finite trifactorised groups and $\pi$-decomposability

Bull. Austral. Math. Soc., 97 (2):218-228, 2018

doi:10.1017/S0004972717001034

Abstract

We derive some structural properties of a trifactorised finite group G = AB = AC = BC, where A, B, and C are subgroups of G, provided that A = Aπ × Aπ’ and B = Bπ × Bπ’ are π-decomposable groups, for a set of primes π.

2010 Mathematics Subject Classification: primary 20D40; secondary 20D20

Keywords: finite group, product of subgroups, π-decomposable group, π-structure.

Paper “2-Engel relations between subgroups” published in J. Algebra

The following paper has been published

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M. P. Gállego, P. Hauck, and M. D. Pérez-Ramos

2-Engel relations between subgroups

J. Algebra, 447:31–55, 2016

https://doi.org/10.1016/j.jalgebra.2015.08.030

Abstract

In this paper we study groups G generated by two subgroups A and B such that 〈a, bis nilpotent of class at most 2 for all aA and  bB . A detailed description of the structure of such groups is obtained, generalizing the classical result of Hopkins and Levi on 2-Engel groups.

2010 Mathematical Subject Classification: Primary 20F45; Secondary 20F18, 20D15, 20F12

Keywords: 2-Engel condition, 2-generated subgroups, L-connection, Nilpotency class