Abstract
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 .
Citation
Michael Bate. Benjamin Martin. Gerhard Röhrle. David I. Stewart. "On Unipotent Radicals of Pseudo-Reductive Groups." Michigan Math. J. 68 (2) 277 - 299, June 2019. https://doi.org/10.1307/mmj/1550480563