Invariable generation of finite simple groups and rational homology of coset posets
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913455563341824 |
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| author | Guralnick, Robert M. Shareshian, John Woodroofe, Russ |
| author_facet | Guralnick, Robert M. Shareshian, John Woodroofe, Russ |
| contents | We show that every finite simple group is generated invariably by a Sylow subgroup and a cyclic group. It follows that that the order complex of the coset poset of an arbitrary finite group has nontrivial reduced rational homology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16319 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Invariable generation of finite simple groups and rational homology of coset posets Guralnick, Robert M. Shareshian, John Woodroofe, Russ Group Theory Algebraic Topology Combinatorics We show that every finite simple group is generated invariably by a Sylow subgroup and a cyclic group. It follows that that the order complex of the coset poset of an arbitrary finite group has nontrivial reduced rational homology. |
| title | Invariable generation of finite simple groups and rational homology of coset posets |
| topic | Group Theory Algebraic Topology Combinatorics |
| url | https://arxiv.org/abs/2312.16319 |