Skip to content

Research at St Andrews

On the growth of generating sets for direct powers of semigroups

Research output: Contribution to journalArticle

Author(s)

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

School/Research organisations

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.

Close

Details

Original languageEnglish
Pages (from-to)116-130
JournalSemigroup Forum
Volume84
Issue number1
Early online date5 Nov 2011
DOIs
Publication statusPublished - 2012

    Research areas

  • Semigroup, Monoid, Direct power, Generating set

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Growth of generating sets for direct powers of classical algebraic structures

    Quick, M. & Ruskuc, N., Aug 2010, In : Journal of the Australian Mathematical Society. 89, 1, p. 105-126 22 p.

    Research output: Contribution to journalArticle

  2. Right Noetherian semigroups

    Miller, C. & Ruskuc, N., 5 Aug 2019, (Accepted/In press) In : International Journal of Algebra and Computation.

    Research output: Contribution to journalArticle

  3. Presentations for subrings and subalgebras of finite co-rank

    Mayr, P. & Ruskuc, N., 20 Jul 2019, (Accepted/In press) In : Quarterly Journal of Mathematics.

    Research output: Contribution to journalArticle

  4. Rationality for subclasses of 321-avoiding permutations

    Albert, M. H., Brignall, R., Ruskuc, N. & Vatter, V., May 2019, In : European Journal of Combinatorics. 78, p. 44-72

    Research output: Contribution to journalArticle

  5. Generating subdirect products

    Mayr, P. & Ruskuc, N., 9 Apr 2019, In : Journal of the London Mathematical Society. Early View

    Research output: Contribution to journalArticle

Related by journal

  1. Generators and presentations for direct and wreath products of monoid acts

    Miller, C., 17 Dec 2018, In : Semigroup Forum. First Online, 24 p.

    Research output: Contribution to journalArticle

  2. Enumerating transformation semigroups

    East, J., Egri-Nagy, A. & Mitchell, J. D., Aug 2017, In : Semigroup Forum. 95, 1, p. 109-125 17 p.

    Research output: Contribution to journalArticle

  3. Ends of semigroups

    Craik, S., Gray, R., Kilibarda, V., Mitchell, J. D. & Ruskuc, N., Oct 2016, In : Semigroup Forum. 93, 2, p. 330-346 17 p.

    Research output: Contribution to journalArticle

  4. The structure of a graph inverse semigroup

    Mesyan, Z. & Mitchell, J. D., 2016, In : Semigroup Forum. First online, 20 p.

    Research output: Contribution to journalArticle

  5. A classification of disjoint unions of two or three copies of the free monogenic semigroup

    Abu-Ghazalh, N., Mitchell, J. D., Péresse, Y. & Ruskuc, N., Aug 2015, In : Semigroup Forum. 91, 1, p. 53-61 9 p.

    Research output: Contribution to journalArticle

ID: 5264895