On groups generated by involutions of a semigroup

James East, Thomas E. Nordahl

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    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
    Pages (from-to)136-162
    Number of pages27
    JournalJournal of Algebra
    Volume445
    DOIs
    Publication statusPublished - 2016

    Keywords

    • algebra
    • automorphisms
    • semigroups

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