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Results tagged with gr.group-theory
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user 19184
Questions about the branch of algebra that deals with groups.
1
vote
1
answer
260
views
Natural actions of quotients of automorphism groups
I've stumbled upon a construction which seems to be very much classical, and yet I found nothing definite about it so far in available sources. Let $\Lambda$ be a normal subgroup of the automorphism g …
- 303
4
votes
The normalizer of $\mathrm{GL}(n,\mathbf Z)$ in $\mathrm{GL}(n,\mathbf Q)$
Let me simplify a bit (if I may) a nice argument by Matthew Emerton, by omitting the part with $p$-reductions. We start as above: let $g \in\mathrm{GL}(n,\mathbf Q)$ normalize $\mathrm{GL}(n,\mathbf Z …
- 303
15
votes
3
answers
1k
views
The normalizer of $\mathrm{GL}(n,\mathbf Z)$ in $\mathrm{GL}(n,\mathbf Q)$
It seems that the normalizer of $H=\mathrm{GL}(n,\mathbf Z)$ in $G=\mathrm{GL}(n,\mathbf Q)$ is "almost" equal to itself, that is,
$$
N_G(\mathrm{GL}(n,\mathbf Z))=Z(G) \cdot \mathrm{GL}(n,\mathbf Z) …
- 303