On One Class of Factorizable Fundamental Inverse Monoids

Abstract

Let G be an arbitrary group of bijections on a finite set and let I(G) denote the set of all partial injective transformations each of which is included in a bijection from G. The set I(G) is a fundamental factorizable inverse semigroup. We study various properties of the semigroup I(G). In particular, we describe the automorphisms of I(G) and obtain necessary and sufficient conditions for each stable order on I(G) to be fundamental or antifundamental.