Topics in topological MI-groups

A many identities group (MI-group, for short) is an algebraic structure which is generalized a monoid with cancellation laws and is endowed with an invertible anti-automorphism representing inversion. In other words, an MI-group is an algebraic structure generalizing the group concept, except most of the elements have no  inverse element. The concept of a topological MI-group, as a preliminary study,  in the paper '' Topological MI-group: Initial study'' was introduced by M. Hol\v capek and N. \v Skorupov\' a, and we  have given a more comprehensive study of this concept in our two recent papers.  This article is a continuation of the effort to develop the theory of topological MI-groups and is focused on the study of  separation axioms and  the isomorphism theorems for topological MI-groups.  Moreover, some conditions under which a MI-subgroup is closed  will be investigated, and finally, the existence of nonnegative  invariant measures on the locally compact MI-groups are introduced.

Keywords:

MI-groups , Monoids , Pseudoidentity elements , Topological MI-groups , Full MI-subgroups