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is injective, where p is a fixed rational prime and n > 1 is odd. Observe that each $p is clearly injective for n = 1, because Ki(0) = 0* and K{{Op) = Op. A much harder problem is whether $ ZP is injective. For n — 1 and F totally real abelian, injectively of $ ® Zp on the subgroup of 0* consisting of those elements congruent to lmodp for each p \ p is equivalent to nonvanishing of the p-adic regulator [Br, C]. As an example of (1) let F be quadratic imaginary. Then is

A 𝑝-adic regulator problem in algebraic 𝐾-theory and group cohomology