5 problems

Metric uniform simplicity for finite metric ultraproducts
arXiv@arxiv
Let $\mathcal{G}=(G_n,\|\cdot\|_n)_{n\in\mathbb{N}}$ be a family of pseudometric groups, and let $({\mathcal G}^*_{\mathrm{met,fin}},\|\cdot\|)$ be its finite metric ultraproduct.…
Conjectureopenmetric-ultraproducts pseudometric-groups simple-groups
0
Uniform torsion conjecture for metric ultraproducts
arXiv@arxiv
Let ${\mathcal G}^*_{\mathrm{met}}$ be a metric ultraproduct. A group has finite exponent, or is uniformly torsion, if there is a common positive integer annihilating every element…
Conjectureopengroup-theory metric-ultraproducts torsion-groups
1
Metric uniform simplicity of simple metric ultraproducts
arXiv@arxiv
Let $({\mathcal G}_{\mathrm{met}},\|\cdot\|)$ be a metric ultraproduct of metric groups. A metric group is metrically uniformly simple if, for every $r>0$ , there is…
Conjectureopenbounded-simplicity metric-ultraproducts simple-groups
1
The soficity conjecture for finitely generated groups
arXiv@arxiv
A group is sofic when every finitely generated group can be homomorphically embedded into a metric ultraproduct of permutation groups. Let $\mathcal{S}=(S_n,\|\cdot\|_H)$ , where…
Conjectureopenmetric-ultraproducts permutation-groups sofic-groups
0
Conjecture on characterization of conjugacy classes with nontrivial fixed-point proportion
arXiv@arxiv
Conjecture on the characterization. The above characterization is false when
Conjectureopenconjugacy-classes finite-groups metric-ultraproducts
0

5 problems

Metric uniform simplicity for finite metric ultraproducts

Uniform torsion conjecture for metric ultraproducts

Metric uniform simplicity of simple metric ultraproducts

The soficity conjecture for finitely generated groups

Conjecture on characterization of conjugacy classes with nontrivial fixed-point proportion