Uncountably many $2$-spherical groups of Kac-Moody type of rank $3$ over $\mathbb{F}_2$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910918019907584 |
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| author | Bischof, Sebastian |
| author_facet | Bischof, Sebastian |
| contents | In this paper we show that Weyl-invariant commutator blueprints of type $(4, 4, 4)$ are faithful. As a consequence we answer a question of Tits from the late $1980$s about twin buildings. Moreover, we obtain the first example of a $2$-spherical Kac-Moody group over a finite field which is not finitely presented. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_17513 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uncountably many $2$-spherical groups of Kac-Moody type of rank $3$ over $\mathbb{F}_2$ Bischof, Sebastian Group Theory Primary: 20E06, 20E42, Secondary: 20F65, 51E42 In this paper we show that Weyl-invariant commutator blueprints of type $(4, 4, 4)$ are faithful. As a consequence we answer a question of Tits from the late $1980$s about twin buildings. Moreover, we obtain the first example of a $2$-spherical Kac-Moody group over a finite field which is not finitely presented. |
| title | Uncountably many $2$-spherical groups of Kac-Moody type of rank $3$ over $\mathbb{F}_2$ |
| topic | Group Theory Primary: 20E06, 20E42, Secondary: 20F65, 51E42 |
| url | https://arxiv.org/abs/2504.17513 |