f-Grouplikes

A grouplike, which has been introduced earlier, is an al- gebraic structure between semigroups and groups and its axioms are generalization of the four group axioms. We observe that every group- like is a homogroup (a semigroup containing an ideal subgroup) with a unique central idempotent. On the other hand, decomposer and as-sociative functions on groups, semigroups and even magmas have been introduced in 2007. In this paper, we introduce special type of group-likes (namely f-grouplike) that is motivated from the both topics. We prove that f-grouplikes is a proper subclass of Class United Grouplikes, and we study some of their properties.