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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2504.17057 |
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| _version_ | 1866913806510194688 |
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| author | Kölsch, Lukas Levinshteyn, Alexandra Tenn, Milan |
| author_facet | Kölsch, Lukas Levinshteyn, Alexandra Tenn, Milan |
| contents | We completely determine the autotopism group of the (as of now) largest family of commutative semifields found by Göloğlu and Kölsch. Since this family of semifields generally does not have large nuclei, this process is considerably harder than for families considered in preceding work. Our results show that all autotopisms are semilinear over the degree 2 subfield and that the autotopism group is always solvable. Using known connections, our results also completely determine the automorphism groups of the associated rank-metric codes and the collineation groups of the associated translation planes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17057 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The autotopism group of a family of commutative semifields Kölsch, Lukas Levinshteyn, Alexandra Tenn, Milan Combinatorics Rings and Algebras We completely determine the autotopism group of the (as of now) largest family of commutative semifields found by Göloğlu and Kölsch. Since this family of semifields generally does not have large nuclei, this process is considerably harder than for families considered in preceding work. Our results show that all autotopisms are semilinear over the degree 2 subfield and that the autotopism group is always solvable. Using known connections, our results also completely determine the automorphism groups of the associated rank-metric codes and the collineation groups of the associated translation planes. |
| title | The autotopism group of a family of commutative semifields |
| topic | Combinatorics Rings and Algebras |
| url | https://arxiv.org/abs/2504.17057 |