Abstract
Consider Wilson's functional equation¶¶\( f(xy) + f(xy^{-1}) = 2f(f)g(y) \), for \( f,g : G \to K \)¶where G is a group and K a field with \( {\rm char}\, K\ne 2 \).¶Aczel, Chung and Ng in 1989 have solved Wilson's equation, assuming that the function g satisfies Kannappan's condition g(xyz) = g(xzy) and f(xy) = f(yx) for all \( x,y,z\in G \).¶In the present paper we obtain the general solution of Wilson's equation when G is a P3-group and we show that there exist solutions different of those obtained by Aczel, Chung and Ng.¶A group G is said to be a P3-group if the commutator subgroup G' of G, generated by all commutators [x,y] := x-1y-1xy, has the order one or two.
Published Version
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