Semigroup Forum, 78, Number 2 (2009), 187-199

In this paper we describe the v-semilatticed inverse semigroups generated by a finite group G. We do this by first constructing the free v -semilatticed inverse semigroup F(G) on the group G. Each v-semilatticed inverse semigroup generated by G is a quotient of F(G) by a v-congruence. We then describe these congruences and their corresponding quotients explicitly in terms of families of subgroups of G.