# On groups generated by involutions of a semigroup

James East, Thomas E Nordahl

Research output: Contribution to journalArticle

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 language English (US) 136-162 27 Journal of Algebra 445 https://doi.org/10.1016/j.jalgebra.2015.08.018 Published - Jan 1 2016

Involution
Si
Semigroup
Binary operation
Symmetric group
Isomorphic
Subgroup
Algebra
Class

### Keywords

• Anti-automorphisms
• Automorphisms
• Involutions
• Semigroups

### ASJC Scopus subject areas

• Algebra and Number Theory

### Cite this

In: Journal of Algebra, Vol. 445, 01.01.2016, p. 136-162.

Research output: Contribution to journalArticle

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