Archivo de la etiqueta: Martínez-Pastor

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 “Prime Power Indices in Factorised Groups” published in Mediterr. J. Math.

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M. J. Felipe, A. Martínez Pastor, and V. M. Ortiz-Sotomayor

Prime power indices in factorised groups.

Mediterr. J. Math., 14(6):Art. 225, 15, 2017

https://doi.org/10.1007/s00605-016-0987-9

Abstract

Let the group G=AB be the product of the subgroups A and B. We determine some structural properties of G when the p-elements in A∪B have prime power indices in G, for some prime p. More generally, we also consider the case that all prime power order elements in A∪B have prime power indices in G. In particular, when G=A=B, we obtain as a consequence some known results.

2010 Mathematics Subject Classification: 20D10, 20D40, 20E45, 20D20

Keywords: Finite groups, Products of groups, Conjugacy classes, Sylow subgroups

Paper “Square-free class sizes in products of groups” published in J. Algebra

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The following paper has been published

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M. J. Felipe, A. Martínez Pastor, and V. M. Ortiz-Sotomayor

Square-free class sizes in products of groups

J. Algebra, 491:190–206, 2017

https://doi.org/10.1016/j.jalgebra.2017.08.007

Abstract

We obtain some structural properties of a factorised group G=AB, given that the conjugacy class sizes of certain elements in A∪B are not divisible by p², for some prime p. The case when G=AB is a mutually permutable product is especially considered.

2010 Mathematical Subject Classification: 20D10, 20D40, 20E45

Keywords: Finite groups, Soluble groups, Products of subgroups, Conjugacy classes