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Questions about the branch of algebra that deals with groups.

3 votes
0 answers
2k views

How big is the center of an orthogonal group?

How big is the center of an arbitrary orthogonal group $O(m,n)$? In the special case of the "circle group" $O(2)$, it's clear that $|\zeta O(2)|$ = 1. In the case of $O(3)$, it seems clear that the c …
soulphysics's user avatar
19 votes
3 answers
5k views

What is the outer automorphism group of SU(n)?

All the automorphisms of $SU(2)$ seem to be inner, which would mean that $\mathrm{Out}$ $SU(2)$ is trivial. Is that correct? Is this true in general $SU(n)$? I can't quite see -- any thoughts would be …
soulphysics's user avatar