Abstract
on U x V, where F i s a Z-rational function from X x Yto Z. In the case where f = O= 95, or more precisely, where there is an open subset S of G containing U, V, and UV, and a Z-valued continuous function g whose restriction to U is 0, to V is 95, and to UV is f , we say that g has an autoaddit ion formula. Our main result relates each g-valued function having an addition formula of our type to a function having an autoaddition formula. More precisely, let f be any ~valued function having an addit ion formula on an open rectangular neighborhood of (e, e) in G x G. Then there is an affine algebraic variety Z over ~t, a Z-valued function g having an autoaddition formula on an open rectangular neighborhood of (e, e) in G x G, and a £-polynomial P on Z such t h a t f = g o P on some neighborhood of e in G.
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