Solvability of the radical in pseudo-finite groups with the DCC on centralizers up to finite index
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909014518923264 |
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| author | Hempel, Nadja Karhumäki, Ulla |
| author_facet | Hempel, Nadja Karhumäki, Ulla |
| contents | The subgroup generated by all solvable normal subgroups in a pseudo-finite group with the descending chain condition on centralizers up to finite index is solvable. Additionally, there is no finitely generated pseudo-finite group whose definable sections satisfy such a chain condition on centralizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03735 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solvability of the radical in pseudo-finite groups with the DCC on centralizers up to finite index Hempel, Nadja Karhumäki, Ulla Group Theory Logic The subgroup generated by all solvable normal subgroups in a pseudo-finite group with the descending chain condition on centralizers up to finite index is solvable. Additionally, there is no finitely generated pseudo-finite group whose definable sections satisfy such a chain condition on centralizers. |
| title | Solvability of the radical in pseudo-finite groups with the DCC on centralizers up to finite index |
| topic | Group Theory Logic |
| url | https://arxiv.org/abs/2605.03735 |