On Cauchy differences of all orders
This paper deals with the problem of characterizing higher order Cauchy differences of mappings on groups and semigroups. Symmetric, first order Cauchy differences f(x + y)-f(x)-f(y) for maps f between groups were characterized by Jessen, Karpf, and Thorup  through the use of first partial Cauchy differences. Our results are similar and extend their result to higher order differences. Our results also extend those of Heuvers  for mappings between vector spaces over the rationals. © 1991 Birkhäuser Verlag.
On Cauchy differences of all orders.
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