LOCAL GROUPS IN FREE GROUPOIDS SATISFYING CERTAIN MONOID IDENTITIES

Abstract

Let G be a (possibly infinite) strongly connected graph and let [Formula: see text] be a set of monoid identities such that any monoid satisfying [Formula: see text] is also a group. Let ℬ be the free groupoid on G satisfying [Formula: see text]. Then, the local groups ℬv, for v ∈ V (G), are all isomorphic to a free group satisfying [Formula: see text]. Furthermore, it is free over a generating set which can be effectively characterized and whose cardinality is the cyclomatic number of the graph G. We also show applications that establish an important connection between free Burnside groups and free Burnside semigroups.