On the maximal submonoid of the monoid consisting of all idempotent probability measures on a topological group

In the paper we investigate topological transformation groups on Tychonoff (in particular, compact Hausdorff) spaces. Using decompositions of given elements of the set of all idempotent probability measures on a given topological group, the group operation represents as a decomposition of Dirac measures. We establish that the space of all idempotent probability measures on a given topological group is a monoid. Then for this monoid we distinguish the maximal submonoid which is a topological group.