Universal groups on semilattices of reversible cancellative semigroups (Q1179488)

A semigroup \(S\) is called left reversible if \(aS\cap bS\neq \emptyset\) for every \(a,b\in S\). Right reversible and reversible semigroups are defined analogously. The pair \((G,\gamma)\) is called the universal group on a semigroup \(S\) if \(G\) is a group, \(\gamma\) a homomorphism and \(\gamma(S)\) a set of group generators of \(G\), and \((G,\gamma)\) is universal in the usual sense with these properties. The author describes the universal group of a semigroup \(S\) which is a semilattice of reversible cancellative semigroups \(S_{\alpha}\) in dependence of the universal groups of the \(S_{\alpha}\). Moreover, the author studies the corresponding universal homomorphisms.