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 language | English |
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Pages (from-to) | 136-162 |
Number of pages | 27 |
Journal | Journal of Algebra |
Volume | 445 |
DOIs | |
Publication status | Published - 2016 |
Keywords
- algebra
- automorphisms
- semigroups