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ON THE CAYLEY SEMIGROUP OF A FINITE APERIODIC SEMIGROUP

Name: ON THE CAYLEY SEMIGROUP OF A FINITE APERIODIC SEMIGROUP
Creator: Avi Mintz
Keywords: FOS: Mathematics, Group Theory (math.GR), 0102 computer and information sciences, 0101 mathematics, Mathematics - Group Theory, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Sep 2009Embargo end date: 01 Jan 2008 English Publisher:World Scientific Pub Co Pte LtJournal:International Journal of Algebra and Computation, volume 19, pages 723-746 (issn: 0218-1967, eissn: 1793-6500,

Authors: Avi Mintz;

doi: 10.1142/s0218196709005378 , 10.48550/arxiv.0808.3415

arXiv: http://arxiv.org/abs/0808.3415

ON THE CAYLEY SEMIGROUP OF A FINITE APERIODIC SEMIGROUP

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Abstract

Let S be a finite semigroup. In this paper, we introduce the functions φs:S* → S*, first defined by Rhodes, given by φs([a1,a2,…,an]) = [sa1,sa1a2,…,sa1a2 ⋯ an]. We show that if S is a finite aperiodic semigroup, then the semigroup generated by the functions {φs}s ∈ S is finite and aperiodic.

Related Organizations

Bar-Ilan University
Israel

Keywords

FOS: Mathematics, Group Theory (math.GR), Mathematics - Group Theory

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