Geodesic
On commutativity of connected groups
Sbornik. Mathematics, Tome 197 (2006) no. 1, pp. 1-21

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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. Bibliography: 43 titles. 
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S. A. Bogatyi; O. D. Frolkina. On commutativity of connected groups. Sbornik. Mathematics, Tome 197 (2006) no. 1, pp. 1-21. http://geodesic.mathdoc.fr/item/SM_2006_197_1_a0/