6533b863fe1ef96bd12c7844

RESEARCH PRODUCT

Some contributions to the theory of transformation monoids

Enric Cosme LlópezAdolfo Ballester-bolinchesP. Jiménez-seral

subject

Classical theoryTransitive relationPure mathematicsAlgebra and Number TheoryConjectureAlgebraic structure010102 general mathematicsPermutation group01 natural sciencesTransformation (music)Development (topology)Mathematics::Category Theory0103 physical sciencesÀlgebra010307 mathematical physics0101 mathematicsMathematics

description

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 [A theory of transformation monoids: combinatorics and representation theory. Electron. J. Combin. 17 (2010), no. 1, Research Paper 164, 56 pp] have been answered. Our results can also be considered as a further development in the hunt for a solution of the Černý conjecture.

yearjournalcountryeditionlanguage
2019-03-01Journal of Algebra
https://doi.org/10.1016/j.jalgebra.2018.12.005