### 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) |
---|---|

Pages (from-to) | 136-162 |

Number of pages | 27 |

Journal | Journal of Algebra |

Volume | 445 |

DOIs | |

State | Published - Jan 1 2016 |

### Fingerprint

### Keywords

- Anti-automorphisms
- Automorphisms
- Involutions
- Semigroups

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Algebra*,

*445*, 136-162. https://doi.org/10.1016/j.jalgebra.2015.08.018

**On groups generated by involutions of a semigroup.** / East, James; Nordahl, Thomas E.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 445, pp. 136-162. https://doi.org/10.1016/j.jalgebra.2015.08.018

}

TY - JOUR

T1 - On groups generated by involutions of a semigroup

AU - East, James

AU - Nordahl, Thomas E

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - Anti-automorphisms

KW - Automorphisms

KW - Involutions

KW - Semigroups

UR - http://www.scopus.com/inward/record.url?scp=84959019423&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959019423&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2015.08.018

DO - 10.1016/j.jalgebra.2015.08.018

M3 - Article

AN - SCOPUS:84959019423

VL - 445

SP - 136

EP - 162

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -