On groups generated by involutions of a semigroup

James East, Thomas E Nordahl

Research output: Contribution to journalArticle

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Abstract

An involution on a semigroup S (or any algebra with an underlying associative binary operation) is a function α. :. S→. S that satisfies α(xy). =α(y)α(x) and α(α(x)). =x for all x, y∈. S. The set I(S) of all such involutions on S generates a subgroup C(S)=〈I(S)〉 of the symmetric group Sym(S) on the set S. We investigate the groups C(S) for certain classes of semigroups S, and also consider the question of which groups are isomorphic to C(S) for a suitable semigroup S.

Original languageEnglish (US)
Pages (from-to)136-162
Number of pages27
JournalJournal of Algebra
Volume445
DOIs
Publication statusPublished - Jan 1 2016

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Keywords

  • Anti-automorphisms
  • Automorphisms
  • Involutions
  • Semigroups

ASJC Scopus subject areas

  • Algebra and Number Theory

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