On groups generated by involutions of a semigroup

JOURNAL OF ALGEBRA

卷:445

Article

East, James¹  Nordahl, Thomas E.² 

[1] Univ Western Sydney, Ctr Res Math, Sch Comp Engn & Math, Penrith, NSW 2751, Australia

[2] Univ Calif Davis, Dept Psychiat & Behav Sci, Imaging Res Ctr, Davis, CA 95616 USA

关键词: Semigroups;    Involutions;    Automorphisms;    Anti-automorphisms;   

DOI  :  10.1016/j.jalgebra.2015.08.018

来源: Elsevier

【 摘 要 】

An involution on a semigroup S (or any algebra with an underlying associative binary operation) is a function alpha : S -> S that satisfies alpha(xy) = alpha(y)alpha(x) and alpha(alpha(z)) = a for all x, y is an element of S. The set I(S) of all such involutions on S generates a subgroup l(S) = < I(S)> of the symmetric group Sym(S) on the set S. We investigate the groups l(S) for certain classes of semigroups S, and also consider the question of which groups are isomorphic to l(S) for a suitable sernigroup S. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free