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Questions about the branch of algebra that deals with groups.

24 votes

Is $SL(n,\mathbb{Z})$ a CAT(0) group?

If n=2, yes: it acts on its Bass-Serre tree. If n>2, no: your group contains distorted elements, i.e. elements conjugated to a proper power of themselves (look at unipotent matrices). Such an elemen …
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