Locally solvable maximal subgroups in division rings
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866913181203431424 |
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| author | Khanh, Huynh Viet Hai, Bui Xuan |
| author_facet | Khanh, Huynh Viet Hai, Bui Xuan |
| contents | Let $D$ be a division ring with center $F$, and $G$ an almost subnormal subgroup of $D^*$. In this paper, we show that if $G$ contains a non-abelian locally solvable maximal subgroup, then $D$ must be a cyclic algebra of prime degree over $F$. Moreover, it is proved that every locally nilpotent maximal subgroup of $G$ is abelian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_04925 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Locally solvable maximal subgroups in division rings Khanh, Huynh Viet Hai, Bui Xuan Rings and Algebras Group Theory Let $D$ be a division ring with center $F$, and $G$ an almost subnormal subgroup of $D^*$. In this paper, we show that if $G$ contains a non-abelian locally solvable maximal subgroup, then $D$ must be a cyclic algebra of prime degree over $F$. Moreover, it is proved that every locally nilpotent maximal subgroup of $G$ is abelian. |
| title | Locally solvable maximal subgroups in division rings |
| topic | Rings and Algebras Group Theory |
| url | https://arxiv.org/abs/1908.04925 |