Johnson, FEA;
(2025)
A Continuous Proof of Zassenhaus's Solubility Theorem.
Vietnam Journal of Mathematics
10.1007/s10013-025-00745-y.
(In press).
Preview |
Text
Johnson_s10013-025-00745-y.pdf Download (378kB) | Preview |
Abstract
A class S of soluble groups is D-bounded when there exists a uniform upper bound for the lengths d(Γ ) of the derived series for Γ ∈ S. A theorem of Zassenhaus (Abh. Math. Semin. Hansisch. Univ. 12, 289–312, 1938) states that for each n the class of soluble subgroups of G L(n, C)is D-bounded. Although Zassenhaus’s theorem is fundamental to the study infinite discrete linear groups the proof given here is located within the theory of continuous groups and the only discrete groups which appear are finite.
| Type: | Article |
|---|---|
| Title: | A Continuous Proof of Zassenhaus's Solubility Theorem |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s10013-025-00745-y |
| Publisher version: | https://doi.org/10.1007/s10013-025-00745-y |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Linear group, Soluble group, Compact Lie group |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10200616 |
Archive Staff Only
 |
View Item |
