f-Grouplikes

A grouplike, which has been introduced earlier, is an algebraic 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 associative 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.