Question

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

score 132 · Answer 1 · 2019-04-08 11:14:02

132

Views

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

Published on 08 Apr 2019 - 11:14

score 440 · Answer 2 · 2019-04-11 00:59:08

440

Views

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

Published on 11 Apr 2019 - 0:59

score 262 · Answer 3 · 2019-04-12 01:31:37

262

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 12 Apr 2019 - 1:31

score 271 · Answer 4 · 2019-04-14 22:21:01

271

Views

Book-recommendations "Profinite Groups"

Published on 14 Apr 2019 - 22:21

score 171 · Answer 5 · 2019-04-15 20:02:19

171

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 15 Apr 2019 - 20:02

score 113 · Answer 6 · 2019-04-21 20:18:15

113

Views

Elements conjugate in profinite completion

Published on 21 Apr 2019 - 20:18

score 917 · Answer 7 · 2019-04-23 19:23:00

917

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 23 Apr 2019 - 19:23

score 3.3k · Answer 8 · 2019-04-29 23:55:47

3.3k

Views

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

Published on 29 Apr 2019 - 23:55

score 68 · Answer 9 · 2019-05-04 17:07:49

68

Views

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

Published on 04 May 2019 - 17:07

score 71 · Answer 10 · 2019-05-09 08:39:09

71

Views

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

Published on 09 May 2019 - 8:39

score 182 · Answer 11 · 2019-05-09 17:09:31

182

Views

Subset of a subgroup is not closed under group actions

Published on 09 May 2019 - 17:09

score 60 · Answer 12 · 2019-05-10 15:41:06

60

Views

Two versions of Baire Category Theorem for Profinite Groups

Published on 10 May 2019 - 15:41

score 701 · Answer 13 · 2019-05-13 08:29:35

701

Views

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

Published on 13 May 2019 - 8:29

score 539 · Answer 14 · 2019-05-20 13:56:12

539

Views

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

Published on 20 May 2019 - 13:56

score 100 · Answer 15 · 2019-05-27 17:44:26

100

Views

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

Published on 27 May 2019 - 17:44

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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