Finite subgroups of \(\vee \)-semilatticed inverse semigroups (Q1014256)

The main purpose of this paper is to describe the \(\vee\)-semilatticed inverse semigroups generated by a finite group \(G\). This is done in two steps; first by constructing the free \(\vee\)-semilatticed inverse semigroup of \({\mathcal F}(G)\) on \(G\); second by describing the \(\vee\)-congruences on \({\mathcal F}(G)\). Since every \(\vee\)-semilatticed inverse semigroup generated by \(G\) is a quotientient of \({\mathcal F}(G)\) by a \(\vee\)-congruence, the authors study the properties of these congruences and describe their corresponding quotients explicitly in terms of subgroups of \(G\).