On groups generated by involutions of a semigroup
Group Theory
2015-09-16 v2
Abstract
An involution on a semigroup S (or any algebra with an underlying associative binary operation) is a function f:S->S that satisfies f(xy)=f(y)f(x) and f(f(x))=x for all x,y in 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.
Keywords
Cite
@article{arxiv.1505.02384,
title = {On groups generated by involutions of a semigroup},
author = {James East and Thomas E. Nordahl},
journal= {arXiv preprint arXiv:1505.02384},
year = {2015}
}
Comments
V2 - fixed typo, added some references - 19 pages, 1 table