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Results tagged with gr.group-theory
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user 717
Questions about the branch of algebra that deals with groups.
14
votes
Quotient of a Hausdorff topological group by a closed subgroup
In fact, an even stronger statement holds: If $G$ is a topological group and $H$ is an (abstract) subgroup, then $G/H$ is Hausdorff if and only if $H$ is closed (cf Bourbaki, General Topology, III.2.5 …
- 5,243
8
votes
2
answers
1k
views
(Non-trivial) presentation of general linear and symplectic group over Z/mZ?
I know that there exists a nice presentation (generators and relations) of the general linear group over a finite field (by Steinberg, I think). Is there also a nice presentation of $GL(n,\mathbb{Z}/m …
- 5,243
6
votes
2
answers
2k
views
Classification of finite complex reflection groups
Background:
Let $K$ be a field and let $V$ be a finite-dimensional $K$-vector space. A pseudoreflection (or usually imprecisely just reflection) in $V$ is an element $1 \neq s \in \mathrm{GL}(V)$ fix …
- 5,243
3
votes
2
answers
688
views
Automorphisms of the totally ordered group $\mathbb{Z}{^n}$ with lexicographical order
It is easy to see that the totally ordered group $\mathbb{Z}$ (the integers) with the natural order has no non-trivial automorphisms. Is this also true for $\mathbb{Z}^n$ with the lexicographical orde …
- 5,243