# Tagged Questions

0answers
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### Semisimple part of a nilpotent connected affine algebraic group

These notes on affine algebraic groups mention the following theorem. Let $G$ be a connected nilpotent affine algebraic group (over an algebraically closed field $k$), and denote $G_s$ and $G_u$ ...
1answer
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### Mal'cev completion of nilpotent groups

Is the $\mathbb{R}$-Mal'cev completion of a finitely generated torsion free nilpotent group connected and simply connected?. Thanks!
1answer
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### Question about $S_\infty$ or $Aut(\mathbb{N})$

I have been reading a little Kechris and other random Polish group books, and have come across a question I just can't wrap my mind around. Show that $S_\infty$ or $Aut(\mathbb{N})$ the set of all ...
2answers
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### For a topological group $G$ and a subgroup $H$, is it true that $[\overline{H}, \overline{H}] = \overline{[H,H]}$? What about algebraic groups?

When discussing with awllower about this question, I begin to think about another one: For a topological group $G$ and a subgroup $H$, is it true that \$[\overline{H}, \overline{H}] = ...
2answers
300 views

### Is it true that under the Zariski topology, a subset is dense if and only if it is a nonempty open subset

Is it true that under the Zariski topology, a subset is dense if and only if it is a nonempty open subset? I know this is true in one direction, i.e., any nonempty open subset is dense, but how ...