On the growth of generating sets for direct powers of semigroups

James T. Hyde, Nicholas J. Loughlin, Martyn Quick, Nik Ruškuc, Alistair Wallis

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish
Pages (from-to)116-130
Number of pages15
JournalSemigroup Forum
Volume84
Issue number1
DOIs
Publication statusPublished - Feb 2012

Keywords

  • Semigroup
  • Monoid
  • Direct Power
  • Generating Set

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