{"user_id":"106729","external_id":{"arxiv":["arXiv:2508.15506"]},"year":"2025","_id":"63569","citation":{"chicago":"Bischof, Sebastian, and Timothée Marquis. “Describing the Nub in Maximal Kac-Moody Groups,” 2025.","apa":"Bischof, S., &#38; Marquis, T. (2025). <i>Describing the nub in maximal Kac-Moody groups</i>.","short":"S. Bischof, T. Marquis, (2025).","bibtex":"@article{Bischof_Marquis_2025, title={Describing the nub in maximal Kac-Moody groups}, author={Bischof, Sebastian and Marquis, Timothée}, year={2025} }","ama":"Bischof S, Marquis T. Describing the nub in maximal Kac-Moody groups. Published online 2025.","mla":"Bischof, Sebastian, and Timothée Marquis. <i>Describing the Nub in Maximal Kac-Moody Groups</i>. 2025.","ieee":"S. Bischof and T. Marquis, “Describing the nub in maximal Kac-Moody groups.” 2025."},"title":"Describing the nub in maximal Kac-Moody groups","type":"preprint","date_updated":"2026-01-12T14:33:08Z","date_created":"2026-01-12T14:12:09Z","abstract":[{"text":"Let $G$ be a totally disconnected locally compact (tdlc) group. The contraction group $\\mathrm{con}(g)$ of an element $g\\in G$ is the set of all $h\\in G$ such that $g^n h g^{-n} \\to 1_G$ as $n \\to \\infty$. The nub of $g$ can then be characterized as the intersection $\\mathrm{nub}(g)$ of the closures of $\\mathrm{con}(g)$ and $\\mathrm{con}(g^{-1})$.\r\n Contraction groups and nubs provide important tools in the study of the structure of tdlc groups, as already evidenced in the work of G. Willis. It is known that $\\mathrm{nub}(g) = \\{1\\}$ if and only if $\\mathrm{con}(g)$ is closed. In general, contraction groups are not closed and computing the nub is typically a challenging problem.\r\n Maximal Kac-Moody groups over finite fields form a prominent family of non-discrete compactly generated simple tdlc groups. In this paper we give a complete description of the nub of any element in these groups.","lang":"eng"}],"language":[{"iso":"eng"}],"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"status":"public","author":[{"first_name":"Sebastian","id":"106729","last_name":"Bischof","full_name":"Bischof, Sebastian"},{"first_name":"Timothée","last_name":"Marquis","full_name":"Marquis, Timothée"}]}