Archivo de la etiqueta: Products of groups

Paper «Products of groups and class sizes of π-elements» published in Mediterr. J. Math.

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M. J. Felipe, A. Martínez-Pastor, V. M. Ortiz-Sotomayor.
Products of groups and class sizes of π-elements.
Mediterr. J. Math., 17(1):Paper No. 15, 20, 2020.

doi:10.1007/s00009-019-1444-5

Abstract

We provide structural criteria for some finite factorised groups G=AB when the conjugacy class sizes in G of certain π-elements in A ∪ B are either π-numbers or π′-numbers, for a set of primes π. In particular, we extend for products of groups some earlier results.

2020 Mathematics Subject Classification: 20D10, 20D40, 20E45, 20D20

Keywords: finite group; products of groups; conjugacy classes, π-structure

Paper «Zeros of irreducible characters in factorized groups» published in Ann. Mat. Pura Appl. (4)

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M. J. Felipe, A. Martínez-Pastor, V. M. Ortiz-Sotomayor.
Zeros of irreducible characters in factorised groups.
Ann. Mat. Pura Appl. (4), 198(1):129–142, 2019.

doi:10.1007/s10231-018-0765-5

Abstract

An element g of a finite group G is said to be vanishing in G if there exists an irreducible character χ of G such that χ(g) = 0; in this case, g is also called a zero of G. The aim of this paper is to obtain structural properties of a factorised group G = AB when we impose some conditions on prime power order elements g ∈ A ∪ B which are (non-)vanishing in G.

2010 Mathematics Subject Classification: 20D40, 20C15, 20E45

Keywords: Finite groups, products of groups, irreducible characters, conjugacy classes, vanishing elements

Paper “Some Results on Products of Finite Groups” published in Bull. Malays. Math. Sci. Soc.

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Adolfo Ballester-Bolinches, Luis M. Ezquerro, A. A. Heliel, and M. M. Al-Shomrani

Some results on products of finite groups

Bull. Malays. Math. Sci. Soc., 40(3):1341–1351, 2017

https://doi.org/10.1007/s40840-015-0111-7

Abstract

Subgroups A and B of a finite group are said to be mutually permutable (respectively, M-permutable and sn-permutable) if A permutes with every subgroup (respectively, every maximal subgroup and every subnormal subgroup) of B and viceversa. If every subgroup of A permutes with every subgroup of B, then the product is said to be totally permutable. These kinds of products have received much attention in the last twenty years. The aim of this paper is to analyse the behaviour of finite pairwise mutually permutable, mutually M-permutable, mutually sn-permutable and totally permutable products with respect to certain classes of groups including the supersoluble groups, widely supersoluble groups, and also the classes of PST-, PT– and T-groups.

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

Keywords: Finite group, Permutability, Products of groups,  Supersoluble group