Unisingular subgroups of symplectic group $Sp_{2n}(2)$ for $2n<250$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916109218742272 |
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| author | Zalesski, Alexandre |
| author_facet | Zalesski, Alexandre |
| contents | A linear group is called unisingular if every element of it has eigenvalue 1. A certain aspect of the theory of abelian varieties requires the knowledge of unisingular irreducible subgroups of the symplectic groups over the field of two elements. A more special, but an important question is on the existence of such subgroups in the symplectic groups of particular degree. We answer this question for almost all degrees $2n<250$, specifically, the question remains open only 7 values of $n$. Additionally, the paper contains results of general nature on the structure of unisingular irreducible linear groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_16075 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unisingular subgroups of symplectic group $Sp_{2n}(2)$ for $2n<250$ Zalesski, Alexandre Group Theory 11G10, 11F80, 20C33, 20H30 A linear group is called unisingular if every element of it has eigenvalue 1. A certain aspect of the theory of abelian varieties requires the knowledge of unisingular irreducible subgroups of the symplectic groups over the field of two elements. A more special, but an important question is on the existence of such subgroups in the symplectic groups of particular degree. We answer this question for almost all degrees $2n<250$, specifically, the question remains open only 7 values of $n$. Additionally, the paper contains results of general nature on the structure of unisingular irreducible linear groups. |
| title | Unisingular subgroups of symplectic group $Sp_{2n}(2)$ for $2n<250$ |
| topic | Group Theory 11G10, 11F80, 20C33, 20H30 |
| url | https://arxiv.org/abs/2401.16075 |