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18 votes
0 answers
734 views

How boundedly generated is $SL_3(\mathbb{Z})$?

The group $G = \mathrm{SL}_3(\mathbb{Z})$ is known to be boundedly generated, that is, there exists some $m \in \mathbb{N}$, and $g_1, \dots, g_m \in G$ such that we have the following equality of ...
Pablo's user avatar
  • 11.3k
12 votes
2 answers
341 views

Which $K$-groups $K(C^*_r(G))$ are computed?

We have the Pimsner-Voiculescu exact sequences and the Baum-Connes map for possible computation of the $K$-theory of the reduced group $C^*$-algebra $C^*_r(G)$ for a topological, locally compact, ...
hänsel's user avatar
  • 685
10 votes
3 answers
725 views

Reduction mod $n$ of symplectic group

Let $g,n$ be positive integers, is there a reference that $\mathrm{Sp}(2g,\mathbb{Z})\to\mathrm{Sp}(2g,\mathbb{Z}/n\mathbb{Z})$ is surjection? The only reference I could find is lemma 5.16 in Deligne–...
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