The inverse monoid of local automorphisms of the quaternion group

Abstract

A local automorphism of the semigroup S is defined as an isomorphism between its two subsemigroups. The set of all local automorphisms of the semigroup S relative to the operation of composition forms an inverse monoid of local automorphisms. In the current theses we present some properties of the inverse monoid of local automorphisms of the quaternion group.