Blocks whose defect groups are Suzuki $2$-groups
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910602250682368 |
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| author | Eaton, Charles W. |
| author_facet | Eaton, Charles W. |
| contents | We classify up to Morita equivalence all blocks whose defect groups are Suzuki $2$-groups. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field, and in fact holds up to basic Morita equivalence. As a consequence Donovan's conjecture holds for Suzuki $2$-groups. A corollary of the proof is that Suzuki Sylow $2$-subgroups of finite groups with no nontrivial odd order normal subgroup are trivial intersection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04028 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Blocks whose defect groups are Suzuki $2$-groups Eaton, Charles W. Group Theory Representation Theory 20C20 We classify up to Morita equivalence all blocks whose defect groups are Suzuki $2$-groups. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field, and in fact holds up to basic Morita equivalence. As a consequence Donovan's conjecture holds for Suzuki $2$-groups. A corollary of the proof is that Suzuki Sylow $2$-subgroups of finite groups with no nontrivial odd order normal subgroup are trivial intersection. |
| title | Blocks whose defect groups are Suzuki $2$-groups |
| topic | Group Theory Representation Theory 20C20 |
| url | https://arxiv.org/abs/2401.04028 |