Jensen's functional equation on groups, II

  title={Jensen's functional equation on groups, II},
  author={Che Tat Ng},
  journal={aequationes mathematicae},
Summary.A natural extension of Jensen's functional equation on the real line is the equation $ f(xy)+f(xy^{-1}) = 2f(x) $ where f maps a group G into an abelian group H. When normalized, it defines semi-homomorphisms. It has been solved when G is free with up to two generators, and when $ G=GL_2(\Bbb Z) $. Here, the results are extended to include all free groups and $ GL_n(\Bbb Z),\ n\geq 3 $.