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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.17145 |
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| _version_ | 1866917598986240000 |
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| author | He, Jiawei Li, Xiaogang |
| author_facet | He, Jiawei Li, Xiaogang |
| contents | Recent classification of $\frac{3}{2}$-transitive permutation groups leaves us with six families of groups which are $2$-transitive, or Frobenius, or one-dimensional affine, or the affine solvable subgroups of $ \mathrm{AGL}(2, q)$, or special projective linear group $\mathrm{PSL}(2, q)$, or $\mathrm{PΓL}(2, q)$, where $q=2^p $ with $p$ prime. According to a case by case analysis, we prove that the endomorphism ring of the natural permutation module for a $\frac{3}{2}$-transitive permutation group is a symmetric algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17145 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The endomorphism rings of permutation modules of $\frac{3}{2}$-transitive permutation groups He, Jiawei Li, Xiaogang Group Theory Recent classification of $\frac{3}{2}$-transitive permutation groups leaves us with six families of groups which are $2$-transitive, or Frobenius, or one-dimensional affine, or the affine solvable subgroups of $ \mathrm{AGL}(2, q)$, or special projective linear group $\mathrm{PSL}(2, q)$, or $\mathrm{PΓL}(2, q)$, where $q=2^p $ with $p$ prime. According to a case by case analysis, we prove that the endomorphism ring of the natural permutation module for a $\frac{3}{2}$-transitive permutation group is a symmetric algebra. |
| title | The endomorphism rings of permutation modules of $\frac{3}{2}$-transitive permutation groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2402.17145 |