Non-existence of abelian maximal subgroups in cyclic division algebras
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917470701355008 |
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| author | Khanh, Huynh Viet |
| author_facet | Khanh, Huynh Viet |
| contents | We prove that no cyclic division algebra (in the sense of Dickson) admits an abelian maximal subgroup in its multiplicative group. This settles a special case of a long-standing conjecture of Akbari--Mahdavi-Hezavehi--Mahmudi and complements earlier results on locally nilpotent maximal subgroups and provides a new malnormality criterion for maximal subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28341 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-existence of abelian maximal subgroups in cyclic division algebras Khanh, Huynh Viet Group Theory 16K20 We prove that no cyclic division algebra (in the sense of Dickson) admits an abelian maximal subgroup in its multiplicative group. This settles a special case of a long-standing conjecture of Akbari--Mahdavi-Hezavehi--Mahmudi and complements earlier results on locally nilpotent maximal subgroups and provides a new malnormality criterion for maximal subgroups. |
| title | Non-existence of abelian maximal subgroups in cyclic division algebras |
| topic | Group Theory 16K20 |
| url | https://arxiv.org/abs/2603.28341 |