MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have a doubt.

Borel computed the rank of the higher algebraic k-theory of $\mathbb{Z}$:

$rank(K_n)(\mathbb{Z})= 1$ if $n\equiv1 mod4$, otherwise this rank is equal to 0.

On the other hand Bjorn Jahren proved for any finite group $G$ that

$rank(K_n(\mathbb{Z}[G]))=c$ if $n\equiv3 mod4$, where c is the number of irreductible complex representation of G.

If I let $G=1$, then I have that $rank(K_n)(\mathbb{Z})= 1$ if $n\equiv3 mod4$...

this is a contradiction with Borel's result. What happened here? Am I wrong? (I hope so)

share|cite|improve this question
Maybe you have misunderstood the statement and $c$ is the number of complex representations that are not real. – Tom Goodwillie Apr 24 '12 at 22:24
A very naive mistake I think. Thank you – Luis Jorge Apr 24 '12 at 22:41

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.