Realizability of fusion systems by discrete groups: II
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912390012993536 |
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| author | Broto, Carles Levi, Ran Oliver, Bob |
| author_facet | Broto, Carles Levi, Ran Oliver, Bob |
| contents | We compare four different types of realizability for saturated fusion systems over discrete $p$-toral groups. For example, when $G$ is a locally finite group all of whose $p$-subgroups are artinian (hence discrete $p$-toral), we show that it has ``weakly Sylow'' $p$-subgroups and give explicit constructions of saturated fusion systems and associated linking systems associated to $G$. We also show that a fusion system over a discrete $p$-toral group $S$ is saturated if its set of morphisms is closed under a certain topology and the finite subgroups of $S$ satisfy the saturation axioms, and prove a version of the Cartan-Eilenberg stable elements theorem for locally finite groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Realizability of fusion systems by discrete groups: II Broto, Carles Levi, Ran Oliver, Bob Group Theory Algebraic Topology 20D20, 20F50 We compare four different types of realizability for saturated fusion systems over discrete $p$-toral groups. For example, when $G$ is a locally finite group all of whose $p$-subgroups are artinian (hence discrete $p$-toral), we show that it has ``weakly Sylow'' $p$-subgroups and give explicit constructions of saturated fusion systems and associated linking systems associated to $G$. We also show that a fusion system over a discrete $p$-toral group $S$ is saturated if its set of morphisms is closed under a certain topology and the finite subgroups of $S$ satisfy the saturation axioms, and prove a version of the Cartan-Eilenberg stable elements theorem for locally finite groups. |
| title | Realizability of fusion systems by discrete groups: II |
| topic | Group Theory Algebraic Topology 20D20, 20F50 |
| url | https://arxiv.org/abs/2505.16375 |