On finite groups with soluble centralisers
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909911528505344 |
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| author | Grazian, Valentina Monetta, Carmine Tracey, Gareth |
| author_facet | Grazian, Valentina Monetta, Carmine Tracey, Gareth |
| contents | We classify finite groups in which the centralisers of certain non-central elements are soluble. This includes a full structural description of groups whose non-central element centralisers are all soluble, and a reduction theorem for the case in which all non-central $π$-elements have soluble centralisers, for a suitable collection $π$ of primes. Our results yield further descriptions under mild local conditions and have applications to groups with soluble involution centralisers, as well as to questions concerning non-commuting graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14723 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On finite groups with soluble centralisers Grazian, Valentina Monetta, Carmine Tracey, Gareth Group Theory 20D20, 20D30, 20D06, 20J06, 05C25 We classify finite groups in which the centralisers of certain non-central elements are soluble. This includes a full structural description of groups whose non-central element centralisers are all soluble, and a reduction theorem for the case in which all non-central $π$-elements have soluble centralisers, for a suitable collection $π$ of primes. Our results yield further descriptions under mild local conditions and have applications to groups with soluble involution centralisers, as well as to questions concerning non-commuting graphs. |
| title | On finite groups with soluble centralisers |
| topic | Group Theory 20D20, 20D30, 20D06, 20J06, 05C25 |
| url | https://arxiv.org/abs/2511.14723 |