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Let p be a rational prime and let G be an elementary abelian p-group, In this note we will show that a lower bound for the p-rank of the finite 1 group Kz(ZG ) can be determined by using results of Bloch [4] and van der Kallen [14] on Kz of truncated polynomial rings. Roughly speaking, we show that the p-rank of K2(~G) grows exponentially with the rank of G. In particular, the "pseudoisotopy" group Wh2(G) (cf. [7,8,16]) is non-trivial if G has rank at least 2.There is no reason to suppose that these estimates give the precise orders of Kz(2~G ) and Whz(G ). The only exact computations known to the authors are those of Dunwoody [6] for G cyclic of order 2 or 3. He shows that K2(2~G) is an elementary abelian 2-group of rank 2 if G has order 2 and of rank 1 if G has order 3. In both cases Whz(G ) is trivial, IfR is a commutative ring and A is a subring of R, f2~/A will denote the module of K~ihler differentials of R considered as an algebra over A and R* will denote the group of units of R. Q will denote the rational numbers and IFq a finite field with q elements. The p-rank of an abelian group G is dimvp (G(X')IFpt. §t
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