Archivo por meses: enero 2019

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 contributions to the theory of transformation monoids» published in J. Algebra

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A. Ballester-Bolinches, E. Cosme-Llópez, P. Jiménez-Seral.

Some contributions to the theory of transformation monoids

J. Algebra., 522:31-60, 2019

doi:10.1016/j.jalgebra.2018.12.005

Abstract

The aim of this paper is to present some contributions to the theory of finite transformation monoids. The dominating influence that permutation groups have on transformation monoids is used to describe and characterise transitive transformation monoids and primitive transitive transformation monoids. We develop a theory that not only includes the analogs of several important theorems of the classical theory of permutation groups but also contains substantial information about the algebraic structure of the transformation monoids. Open questions naturally arising from the substantial paper of Steinberg (2010) [11] have been answered. Our results can also be considered as a further development in the hunt for a solution of the Černý conjecture.

2010 Mathematics Subject Classification: 16W22, 20M30

Keywords: monoid theory, monoid action, transitive, faithful, primitive