Question

Does the Burnside $\mathbb Q$-algebra $A$ of a group depend only on $\dim_{\mathbb Q}A$?

score 135 · Answer 1 · 2026-04-13 19:51:56

135

Views

Does the Burnside $\mathbb Q$-algebra $A$ of a group depend only on $\dim_{\mathbb Q}A$?

Published on 13 Apr 2026 - 19:51

score 443 · Answer 2 · 2026-04-16 10:46:09

443

Views

If $(X_{i}, \varphi_{ij})$ is a inverse system of nonempty sets and surjective maps, then the inverse limit is nonempty.

Published on 16 Apr 2026 - 10:46

score 265 · Answer 3 · 2026-04-16 00:31:58

265

Views

If $(X_{i}, \varphi_{ij})$ is a inverse system of nonempty sets and surjective maps, then the inverse limit is nonempty (proof verification)

Published on 16 Apr 2026 - 0:31

score 275 · Answer 4 · 2026-04-13 05:08:02

275

Views

Book-recommendations "Profinite Groups"

Published on 13 Apr 2026 - 5:08

score 174 · Answer 5 · 2026-04-14 01:12:31

174

Views

If $H$ is a closed subgroup of a profinte group $G$, then $H$ is the inverse limit of the open subgroups of $G$ containing $H$.

Published on 14 Apr 2026 - 1:12

score 116 · Answer 6 · 2026-04-10 15:48:34

116

Views

Elements conjugate in profinite completion

Published on 10 Apr 2026 - 15:48

score 920 · Answer 7 · 2026-04-12 13:56:49

920

Views

The multiplicative group of units in $\mathbb{Z}_{p}$ is isomorphic to $\mathbb{Z}_{p} \times C_{n}$ with $n=\max\{p-1,2\}$.

Published on 12 Apr 2026 - 13:56

score 3.3k · Answer 8 · 2026-04-09 17:03:51

3.3k

Views

Krull Topology on Galois Groups (two equivalent(?) definitions).

Published on 09 Apr 2026 - 17:03

score 72 · Answer 9 · 2026-04-15 09:31:21

72

Views

Galois group of $\overline{F}/F$

Published on 15 Apr 2026 - 9:31

score 74 · Answer 10 · 2026-04-14 20:01:02

74

Views

A subset $C$ of a pro-finite group is closed iff $C$ is compact

Published on 14 Apr 2026 - 20:01

score 185 · Answer 11 · 2026-04-14 03:38:28

185

Views

Subset of a subgroup is not closed under group actions

Published on 14 Apr 2026 - 3:38

score 64 · Answer 12 · 2026-05-10 17:13:36

64

Views

Two versions of Baire Category Theorem for Profinite Groups

Published on 10 May 2026 - 17:13

score 704 · Answer 13 · 2026-04-13 21:12:28

704

Views

Open normal subgroups of a profinite group form a basis for the open neighborhoods of 1

Published on 13 Apr 2026 - 21:12

score 542 · Answer 14 · 2026-04-12 16:14:49

542

Views

limits of powers of a matrix with entries in p-adic numbers; galois representation of finite fields

Published on 12 Apr 2026 - 16:14

score 103 · Answer 15 · 2026-04-15 07:27:29

103

Views

Show that the $\Gamma_1$ of $\mathrm{SL}_n(\mathbb{Z}_p)$ is pro-$p$ and finitely generated.

Published on 15 Apr 2026 - 7:27

List Question

Does the Burnside $\mathbb Q$-algebra $A$ of a group depend only on $\dim_{\mathbb Q}A$?

If $(X_{i}, \varphi_{ij})$ is a inverse system of nonempty sets and surjective maps, then the inverse limit is nonempty.

If $(X_{i}, \varphi_{ij})$ is a inverse system of nonempty sets and surjective maps, then the inverse limit is nonempty (proof verification)

Book-recommendations "Profinite Groups"

If $H$ is a closed subgroup of a profinte group $G$, then $H$ is the inverse limit of the open subgroups of $G$ containing $H$.

Elements conjugate in profinite completion

The multiplicative group of units in $\mathbb{Z}_{p}$ is isomorphic to $\mathbb{Z}_{p} \times C_{n}$ with $n=\max\{p-1,2\}$.

Krull Topology on Galois Groups (two equivalent(?) definitions).

Galois group of $\overline{F}/F$

A subset $C$ of a pro-finite group is closed iff $C$ is compact

Subset of a subgroup is not closed under group actions

Two versions of Baire Category Theorem for Profinite Groups

Open normal subgroups of a profinite group form a basis for the open neighborhoods of 1

limits of powers of a matrix with entries in p-adic numbers; galois representation of finite fields

Show that the $\Gamma_1$ of $\mathrm{SL}_n(\mathbb{Z}_p)$ is pro-$p$ and finitely generated.

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