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On unipotent radicals of pseudo-reductive groups

Lookup NU author(s): Dr David StewartORCiD

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This is the authors' accepted manuscript of an article that has been published in its final definitive form by Department of Mathematics, University of Michigan, 2019.

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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 p^e and let G denote the Weil restriction of scalars R_{k'/k}(G') of a reductive k'-group G'. When G= \R_{k'/k}(G') we also provide some results on the orders of elements of the unipotent radical \RR_u(G_{\bar k}) of the extension of scalars of G to the algebraic closure \bar k of k.


Publication metadata

Author(s): Bate M, Martin BMS, Roehrle G, Stewart DI

Publication type: Article

Publication status: Published

Journal: Michigan Mathematical Journal

Year: 2019

Volume: 68

Issue: 2

Pages: 277-299

Print publication date: 01/06/2019

Online publication date: 18/02/2019

Acceptance date: 06/09/2018

Date deposited: 10/09/2018

ISSN (print): 0026-2285

ISSN (electronic): 1945-2365

Publisher: Department of Mathematics, University of Michigan

URL: https://doi.org/10.1307/mmj/1550480563

DOI: 10.1307/mmj/1550480563


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