a study of decomposer and related functions on groups

Decomposer functions in algebraic structures are studiedin many recent papers. they have close relations to factorization by twosubsets. also, idempotent endomorphisms form a class of (strong) decomposerfunctions in groups. now, if the algebraic structure is a group,then by introducing a type of local homomorphisms we obtain severalproperties and equivalent conditions for many classes of decomposerfunctions and get a new result regarding to factorization of a group byits two subsets. moreover, we prove existence of (two-sided) decomposertype functions in non-simple groups.