Marginal subsemigroups and commutators in inverse semigroups

Marginal subgroups, introduced by P. Hall, are characteristic subgroups induced by group words. The goal of this paper is to extend the notion to inverse semigroups. Our first main result establishes that these marginal subsemigroups are full inverse subsemigroups. We then examine the special case in which the word is the commutator, showing that the induced marginal inverse subsemigroup coincides with the metacenter, which is a normal inverse subsemigroup. In the process we prove some results about commutators in inverse semigroups and in Clifford semigroups. The paper concludes with several open problems.