All Questions
14 questions
4
votes
0
answers
97
views
Characterization of Vilenkin group
It is shown in [1, Section 1] by C.W. Onneweer that every infinite compact, metrizable, zero-dimensional commutative group is a Vilenkin group. My question is does this implication also hold if we ...
- 85
1
vote
1
answer
209
views
A question about automorphism group of abelian group
Does anyone know any references that describe automorphism group $\operatorname{Aut}(\mathbb R^n\times \mathbb T^m)$? I searched for a long time but couldn't find it.
- 71
2
votes
1
answer
151
views
Topological analogue of an FC group?
By definition, a group is FC if all its conjugacy classes are finite.
Has anything been published about a generalization of the FC property for topological groups?
- 51
2
votes
0
answers
143
views
Regular epi- and mono-morphisms for locally compact (Hausdorff) groups
I am interested in what the regular monomorphisms are in the category of locally compact (for me, always Hausdorff) groups (with continuous group homomorphisms).
It is easy to see that the equaliser (...
- 18.7k
2
votes
1
answer
82
views
Structure of extensions arising in Lie approximation of connected groups
My imperfect understanding is that, by the work of various authors (Gleason, Yamabe, Montgomery, Zippin ...), the following result is known:
Let $G$ be a connected, locally compact, Hausdorff group, ...
- 25.8k
0
votes
1
answer
434
views
Reference request: Any connected Lie group has a countable base for its topology
I am looking for a reference for the assertion in the title. This assertion is proved in a comment of user nfdc23 to this question. Has any proof of this assertion been published?
- 14.2k
13
votes
3
answers
2k
views
Weil's book L'intégration dans les groupes topologiques et ses applications
The book L'intégration dans les groupes topologiques et ses applications published by André Weil in 1940 is regarded as one of the classical references for harmonic analysis on topological groups.
...
user92170
5
votes
1
answer
163
views
Characteristically simple locally compact abelian groups
Say a topological group $G$ is topologically characteristically simple if there does not exist a closed subgroup $1 < K < G$ such that $K$ is invariant under all automorphisms of $G$ (here `...
- 4,728
8
votes
1
answer
229
views
Embedding abelian cancellative Hausdorff topological semigroups into abelian Hausdorff topological groups
An abelian cancellative semigroup embeds (via a semigroup monomorphism) into an abelian group. What about an abelian cancellative Hausdorff topological semigroup that does not embed (via a ...
- 10.5k
6
votes
1
answer
144
views
Continuity of conjugation actions of Polish groups
Let $G$ and $H$ be Polish groups and let $\psi: G \rightarrow H$ be a continuous injective homomorphism such that $\psi(G)$ is normal in $H$. Then $H$ acts on $G$ by conjugation via $\psi$, in other ...
- 4,728
5
votes
1
answer
170
views
Equations and random subgroups in compact groups
EDIT: Here is a more specific question.
Let $G$ be a compact group and let $w$ be a word in $d$ variables. Then the solution set $S$ of the equation of $w=1$ is a closed subset of the product $G^d$ ...
- 4,728
0
votes
0
answers
75
views
The set of (property) elements of a locally compact group is closed
For which properties $(P)$ is the following statement known to be true?
In any locally compact group $G$, the elements of $G$ that satisfy $(P)$ form a closed subset of $G$. In other words, the ...
- 4,728
5
votes
0
answers
107
views
A dynamical property of automorphisms of a locally compact group
Let $G$ be a Hausdorff locally compact group and let $\alpha$ be an automorphism of $G$. Say $\alpha$ is (forwards) topologically recurrent if for all $g \in G$ and all neighbourhoods $O$ of $g$, the ...
- 4,728
9
votes
0
answers
329
views
'Infinitesimal' elements of a topological group
Let $G$ be a topological group, and let $M$ be the intersection of all conjugacy-invariant neighbourhoods of the identity in $G$ (in other words, the set of elements that can be taken arbitarily close ...
- 4,728