Integrals of groups II
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2020
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914814347968512 |
|---|---|
| author | Araújo, João Cameron, Peter J. Casolo, Carlo Matucci, Francesco Quadrelli, Claudio |
| author_facet | Araújo, João Cameron, Peter J. Casolo, Carlo Matucci, Francesco Quadrelli, Claudio |
| contents | An $integral$ of a group $G$ is a group $H$ whose commutator subgroup is isomorphic to $G$. This paper continues the investigation on integrals of groups started in the work arXiv:1803.10179. We study:
(1) A sufficient condition for a bound on the order of an integral for a finite integrable group and a necessary condition for a group to be integrable.
(2) The existence of integrals that are $p$-groups for abelian $p$-groups, and of nilpotent integrals for all abelian groups.
(3) Integrals of (finite or infinite) abelian groups, including nilpotent integrals, groups with finite index in some integral, periodic groups, torsion-free groups and finitely generated groups.
(4) The variety of integrals of groups from a given variety, varieties of integrable groups and classes of groups whose integrals (when they exist) still belong to such a class.
(5) Integrals of profinite groups and a characterization for integrability for finitely generated profinite centreless groups.
(6) Integrals of Cartesian products, which are then used to construct examples of integrable profinite groups without a profinite integral.
We end the paper with a number of open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_13675 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Integrals of groups II Araújo, João Cameron, Peter J. Casolo, Carlo Matucci, Francesco Quadrelli, Claudio Group Theory 20D99, 20D25 An $integral$ of a group $G$ is a group $H$ whose commutator subgroup is isomorphic to $G$. This paper continues the investigation on integrals of groups started in the work arXiv:1803.10179. We study: (1) A sufficient condition for a bound on the order of an integral for a finite integrable group and a necessary condition for a group to be integrable. (2) The existence of integrals that are $p$-groups for abelian $p$-groups, and of nilpotent integrals for all abelian groups. (3) Integrals of (finite or infinite) abelian groups, including nilpotent integrals, groups with finite index in some integral, periodic groups, torsion-free groups and finitely generated groups. (4) The variety of integrals of groups from a given variety, varieties of integrable groups and classes of groups whose integrals (when they exist) still belong to such a class. (5) Integrals of profinite groups and a characterization for integrability for finitely generated profinite centreless groups. (6) Integrals of Cartesian products, which are then used to construct examples of integrable profinite groups without a profinite integral. We end the paper with a number of open problems. |
| title | Integrals of groups II |
| topic | Group Theory 20D99, 20D25 |
| url | https://arxiv.org/abs/2008.13675 |