On groups that can be covered by conjugates of finitely many cyclic or procyclic subgroups
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929699191521280 |
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| author | Barnea, Yiftach Camina, Rachel Ershov, Mikhail Lewis, Mark L. |
| author_facet | Barnea, Yiftach Camina, Rachel Ershov, Mikhail Lewis, Mark L. |
| contents | Given a discrete (resp. profinite) group $G$, we define $NCC(G)$ to be the smallest number of cyclic (resp. procyclic) subgroups of $G$ whose conjugates cover $G$. In this paper we determine all residually finite discrete groups with finite NCC and give an almost complete characterization of profinite groups with finite NCC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_15746 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On groups that can be covered by conjugates of finitely many cyclic or procyclic subgroups Barnea, Yiftach Camina, Rachel Ershov, Mikhail Lewis, Mark L. Group Theory Number Theory primary: 20D15, 20E18, secondary: 20E26, 20E34, 20E45, 20G25 Given a discrete (resp. profinite) group $G$, we define $NCC(G)$ to be the smallest number of cyclic (resp. procyclic) subgroups of $G$ whose conjugates cover $G$. In this paper we determine all residually finite discrete groups with finite NCC and give an almost complete characterization of profinite groups with finite NCC. |
| title | On groups that can be covered by conjugates of finitely many cyclic or procyclic subgroups |
| topic | Group Theory Number Theory primary: 20D15, 20E18, secondary: 20E26, 20E34, 20E45, 20G25 |
| url | https://arxiv.org/abs/2210.15746 |