A study of decomposer and related functions on groups

Abstract

Decomposer functions in algebraic structures are studied in many recent papers.
They have close relations to factorization by (two) subsets. Also,
idempotent endomorphisms form a class of (strong) decomposer functions in groups.
Now, if the algebraic structure is a group, then by introducing a type of local homomorphisms
we obtain several  properties and equivalent conditions for many classes
of decomposer functions and get a new result regarding to factorization of a group by its two subsets.
Moreover, we prove existence of (two-sided)  decomposer type functions in non-simple groups.