On overgroups in \(\text{GL}(n,F)\) over a subfield of \(F\). (English) Zbl 1179.20042
Shum, K. P. (ed.) et al., Advances in algebra and combinatorics. Proceedings of the 2nd international congress in algebra and combinatorics, Guangzhou, China, July 2–4, 2007, Beijing, China, July 6–11, 2007 and Xian, China, July 12–15, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-279-000-2/hbk). 257-273 (2008).
Summary: Let \(F\) be a field and \(K\) a subfield of \(F\). We classify the overgroups in \(\text{GL}(n,F)\) of an \(\text{Sp}(n,K,f_K)\), \(\text{SU}(n,K,f_K)\) or \(\Omega(n,K,Q_K)\) provided that the index \([F:K]\) is not much bigger than the Witt index \(\nu(f_k)\) or \(\nu(Q_K)\).
For the entire collection see [Zbl 1144.05001].
For the entire collection see [Zbl 1144.05001].
MSC:
| 20G15 | Linear algebraic groups over arbitrary fields |
| 20E07 | Subgroup theorems; subgroup growth |
| 20E15 | Chains and lattices of subgroups, subnormal subgroups |
| 20E28 | Maximal subgroups |
