Questions tagged [profinite-groups]
310 questions
21
votes
4 answers
What is the virtue of profinite groups as mathematical objects?
In my own research I use profinite groups quite frequently (for Galois groups and etale fundamental groups). However my use of them amounts to book-keeping: I only care about finite levels (finite Galois extensions; finite covers) and so I take…
James D. Taylor
- 6,178
6
votes
1 answer
Open subgroups of free profinite groups
The following questions popped out while I was preparing a course on profinite groups.
Closed subgroups of free profinite groups are not necessarily profinite free (e.g. the p-sylow subgroups, or the kernel of the map on the maximum p quotient, and…
Lior Bary-Soroker
- 3,282
5
votes
1 answer
Haar measure for profinite groups (reference needed)
I was wondering if anybody knows a good reference book or exposition for Haar measures over profinite groups (with some concrete examples and computations)?
user23860
4
votes
1 answer
Open subgroups of free pro-C groups
This question is related to this mathoverflow question that I've asked recently.
The question rose while I prepared my lectures on Profinite Groups in an advance course in Tel Aviv University. Let $\mathcal{C}$ be a family of finite groups, and $F$…
Lior Bary-Soroker
- 3,282
4
votes
1 answer
Is every countably generated profinite group countably based?
In a profinite group: Does the existence of a countable generating (topologically) set imply the existence of a countable basis for the topology.
Pablo
- 11,229
3
votes
0 answers
Metrisable profinite groups
I do not understand on page 6 of Galois Cohomology from Serre, the comment after exercise 2) part d). He claims that taking G to be the dual of a countably dimensional vector space over $\mathbb{F}_p$ yields an example of a profinite group that is…
Rodolphe
- 31
- 1
3
votes
2 answers
Is every first countable profinite group, second countable?
Is every first countable profinite group actually second countable?
Pablo
- 11,229
2
votes
0 answers
Profinite topology
For a distance fixed prime numbers $p$ and $q$, let $G_p$, $G_q$ and $Sl$ the pseudovarieties of all finite $p$-group, $q$-group and semilattices respectively. Dose the following equality hold?
$Sl*G_p*G_q=(Sl*G_p)\mal G_q$
where $*$ denote the…
user182085
- 421
1
vote
0 answers
dense subgroup in pro v topology
Let $V$ be a extension closed pseudovariety. The pro-$V$ topology on a group $G$ is the unique group topology such that the set of normal subgroups $N$ with $G/N$ in $V$ is a fundamental system of neighborhoods of the identity.
Let $K$ be a finitely…
user182085
- 421