The Michigan Mathematical Journal
- Michigan Math. J.
- Volume 68, Issue 2 (2019), 277-299.
On Unipotent Radicals of Pseudo-Reductive Groups
We establish some results on the structure of the geometric unipotent radicals of pseudo-reductive -groups. In particular, our main theorem gives bounds on the nilpotency class of geometric unipotent radicals of standard pseudo-reductive groups, which are sharp in many cases. A major part of the proof rests upon consideration of the following situation: let be a purely inseparable field extension of of degree , and let denote the Weil restriction of scalars of a reductive -group . When , we also provide some results on the orders of elements of the unipotent radical of the extension of scalars of to the algebraic closure of .
Michigan Math. J., Volume 68, Issue 2 (2019), 277-299.
Received: 24 April 2017
Revised: 7 September 2018
First available in Project Euclid: 18 February 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20G15: Linear algebraic groups over arbitrary fields
Bate, Michael; Martin, Benjamin; Röhrle, Gerhard; Stewart, David I. On Unipotent Radicals of Pseudo-Reductive Groups. Michigan Math. J. 68 (2019), no. 2, 277--299. doi:10.1307/mmj/1550480563. https://projecteuclid.org/euclid.mmj/1550480563