On unipotent radicals of pseudo-reductive groups

M. Bate, B. Martin, G. Rohrle, D.I. Stewart

Research output: Contribution to journalArticlepeer-review

Abstract

We establish some results on the structure of the geometric unipotent radicals of pseudo-reductive k-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 k be a purely inseparable field extension of k of degree pe, and let G denote the Weil restriction of scalars Rk/k(G) of a reductive k-group G. When G = Rk/k(G), we also provide some results on the orders of elements of the unipotent radical Ru(Gk ¯ ) of the extension of scalars of G to the algebraic closure k¯ of k. © 2019 University of Michigan. All rights reserved.
Original languageEnglish
Pages (from-to)277-299
Number of pages23
JournalMichigan Mathematical Journal
Volume68
Issue number2
DOIs
Publication statusPublished - Jun 2019

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