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Results tagged with profinite-groups
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user 82229
0
votes
0
answers
216
views
short exact sequence of profinite groups
Let $A\rightarrow B\rightarrow B/A$ be a short exact sequence of topological groups. Is it true that if there exists a continuous function $B/A\rightarrow B$ (of underlying spaces) such that the compo …
- 1,613
2
votes
0
answers
223
views
lie algebra associated to a profinite group
is there a natural way to associate a Lie algebra (over real numbers or other field) to a profinite group in a functorial way ?
I.e. I'm looking for a functor $L: \mathbf{ProfinGroups}\rightarrow \ma …
- 1,613
0
votes
1
answer
245
views
Subgroup of free profinite group is free profinite?
The question is already in the title.
It is known that any subgroup of a free group is free. My question is:
Is a closed subgroup of a free profinite group is again a free profinite group ?
- 749
1
vote
2
answers
1k
views
Is the absolute Galois group the same as the automorphism group? [closed]
Is the absolute Galois group $\mathrm{Gal}(\overline{\mathbf{Q}}|\mathbf{Q})$ the same as the group $\mathrm{Aut}_{\mathbf{Q}}(\overline{\mathbf{Q}})$ the automorphism group in the category of $\mathb …
- 7,994
11
votes
1
answer
852
views
Dessins d'enfants and absolute Galois group
I would like to know what is the recent progress about the group homomorphism
$$ \mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})\rightarrow \mathrm{Out}(\hat{F_{2}})$$
$\mathrm{Gal}(\overline{\mathbf …
- 11.2k