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On Jensen’s functional equation. (English) Zbl 0755.39008
The following is offered as main result. Let (G,·) and (H,+) be abelian groups, and e the neutral element of (G,·). The solutions f:GH of f(xy)+f(xy -1 )=2f(x), f(e)=0 are exactly the homomorphisms of GH if, and only if, either H has no element of order 2 or [G:G 2 ]2, where G 2 :={x 2 xG}. While this is not true in general for nonabelian groups, a partial result (in the “only if” direction) is presented in this case too.

MSC:
39B52Functional equations for functions with more general domains and/or ranges
References:
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