On Unipotent Radicals of Pseudo-Reductive Groups

Michael Bate, Benjamin Martin, Gerhard Röhrle, David I. Stewart

Research output: Contribution to journalArticle

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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 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(G) of the extension of scalars of G to the algebraic closure k¯ of k.
Original languageEnglish
Pages (from-to)277-299
Number of pages23
JournalThe Michigan Mathematical Journal
Volume68
Issue number2
Early online date18 Feb 2019
DOIs
Publication statusPublished - 1 Jun 2019

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Reductive Group
K-group
Scalar
Nilpotency
Closure
Denote
Restriction
Theorem

Keywords

  • ALGEBRAIC-GROUPS

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On Unipotent Radicals of Pseudo-Reductive Groups. / Bate, Michael; Martin, Benjamin; Röhrle, Gerhard; Stewart, David I.

In: The Michigan Mathematical Journal, Vol. 68, No. 2, 01.06.2019, p. 277-299.

Research output: Contribution to journalArticle

Bate, Michael ; Martin, Benjamin ; Röhrle, Gerhard ; Stewart, David I. / On Unipotent Radicals of Pseudo-Reductive Groups. In: The Michigan Mathematical Journal. 2019 ; Vol. 68, No. 2. pp. 277-299.
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