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Results tagged with absolute-galois-group
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user 50351
19
votes
Accepted
Classify all the fields with abelian absolute Galois group
Geyer in Unendliche algebraische Zahlkörper, über denen jede Gleichung auflösbar von beschränkter Stufe ist, Satz 1.13 and the paragraph after that, gives a full characterization of which abelian prof …
- 2,051
3
votes
Accepted
Relation between $G_{\mathbb{Q}_p}$ for different primes
As noted in the remarks above, there are different (although conjugate) embeddings $G_{\mathbb{Q}_p}\rightarrow G_\mathbb{Q}$. Let us fix one of them and denote its image by $G_p$.
If we fix prime num …
- 2,051
8
votes
Accepted
Commutator subgroup of the absolute Galois group - a closed subgroup
No, the abstract commutator subgroup $[G_K,G_K]$ of the absolute Galois group $G_K$ of a number field $K$ is never closed:
Write $[G,G]$ for the commutator subgroup of $G$ as an abstract group,
and $c …
- 2,051