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On unipotent radicals of pseudo-reductive groups

Lookup NU author(s): Dr David Stewart

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This is the authors' accepted manuscript of an article that has been accepted and is due to be published in its final definitive form by Department of Mathematics, University of Michigan, 2018.

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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: In Press

Journal: Michigan Mathematical Journal

Year: 2018

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


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