Amalgams of finite inverse semigroups. (Q1772442)

It is proved that the word problem is decidable for an amalgamated free product of finite inverse semigroups in the category of inverse semigroups. (If the word ``inverse'' is dropped throughout this sentence the resulting statement is known to be false.) The constructions which comprise the ingredients of the proof are complicated but are derived in part from an approach of Bennett of the Schützenberger automata for the amalgamated free product of a certain class of amalgams of inverse semigroups.