# 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 AB 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 «On products of groups and indices not divisible by a given prime» published in Monatsh. Math.

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María José Felipe, Lev S. Kazarin, Ana Martínez-Pastor, and Víctor Sotomayor.
On products of groups and indices not divisible by a given prime.
Comm. Algebra, 193(4):811–827, 2020.

doi:10.1007/s00605-020-01446-z

Abstract

Let the group G = AB be the product of subgroups A and B, and let p be a prime. We prove that p does not divide the conjugacy class size (index) of each p-regular element of prime power order xAB if and only if G is p-decomposable, i.e. G=Op(G) × Op’(G).

2020 Mathematics Subject Classification: 20D40, 20E45, 20D20, 20D60

Keywords: Finite groups; products of groups; conjugacy classes; p-structure; prime graph; almost simple groups

# 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 gAB 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 «On finite groups with square-free conjugacy class sizes» published in Int. J. Group Theory

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María José Felipe, Ana Martínez-Pastor, Víctor-Manuel Ortiz-Sotomayor

On finite groups with square-free conjugacy class sizes

Int. J. Group Th., 7 (2):17-24, 2018

doi:10.22108/ijgt.2017.21475

Abstract

We report on finite groups having square-free conjugacy class sizes, in particular in the framework of factorised groups.

2010 Mathematics Subject Classification: Primary: 20E45. Secondary: 20D40, 20D10, 20D20

Keywords: finite group, conjugacy class, factorised group

# 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 AB have prime power indices in G, for some prime p. More generally, we also consider the case that all prime power order elements in AB 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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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 AB are not divisible by , 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