On commutativity of connected groups

In this paper the question is studied of the possibility of obtaining a converse of the well-known theorem of Scheffer on homotopic representation of a given map of a compact connected group into a locally compact Abelian group by a (unique) homomorphism. Namely, several conditions are found under which the existence of a representing homomorphism (its uniqueness) implies that the group is Abelian.
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