On the growth of generating sets for direct powers of semigroups

James Thomas Hyde; Nicholas Loughlin; Martyn Quick; Nik Ruskuc; Alistair Wallis

doi:10.1007/s00233-011-9352-4

On the growth of generating sets for direct powers of semigroups

James Thomas Hyde, Nicholas Loughlin, Martyn Quick, Nik Ruskuc, Alistair Wallis

Research output: Contribution to journal › Article › peer-review

Abstract

For a semigroup S its d-sequence is d(S) = (d₁, d₂, d₃, . . .), where di is the smallest number of elements needed to generate the ith direct power of S. In this paper we present a number of facts concerning the type of growth d(S) can have when S is an infinite semigroup, comparing them with the corresponding known facts for infinite groups, and also for finite groups and semigroups.

Original language	English
Pages (from-to)	116-130
Journal	Semigroup Forum
Volume	84
Issue number	1
Early online date	5 Nov 2011
DOIs	https://doi.org/10.1007/s00233-011-9352-4
Publication status	Published - 2012

Keywords

Semigroup
Monoid
Direct power
Generating set

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10.1007/s00233-011-9352-4

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This is an author version of this article. The original publication (c) Springer Science+ Business Media, LLC 20011 is available at www.springerlink.com
Accepted author manuscript, 171 KB

Automata Languages Decidability: Automata, Languages, Decidability in Algebra
Ruskuc, N. (PI) & Quick, M. (CoI)
EPSRC
1/03/10 → 31/05/14
Project: Standard

Cite this

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AU - Wallis, Alistair

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KW - Semigroup

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KW - Generating set

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On the growth of generating sets for direct powers of semigroups

Abstract

Keywords

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Projects

Automata Languages Decidability: Automata, Languages, Decidability in Algebra

Cite this