A characterisation of the range of a homomorphism between two commutative group algebras is presented which implies, among other things, that this range is closed. The work relies mainly on the characterisation of such homomorphisms achieved by P.~J.~Cohen.

MSC Classifications:

43A22, 22B10, 46J99 show english descriptions Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
Structure of group algebras of LCA groups
None of the above, but in this section 43A22 - Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
22B10 - Structure of group algebras of LCA groups
46J99 - None of the above, but in this section

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