The Michigan Mathematical Journal

On Unipotent Radicals of Pseudo-Reductive Groups

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

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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.

Article information

Michigan Math. J., Volume 68, Issue 2 (2019), 277-299.

Received: 24 April 2017
Revised: 7 September 2018
First available in Project Euclid: 18 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20G15: Linear algebraic groups over arbitrary fields


Bate, Michael; Martin, Benjamin; Röhrle, Gerhard; Stewart, David I. On Unipotent Radicals of Pseudo-Reductive Groups. Michigan Math. J. 68 (2019), no. 2, 277--299. doi:10.1307/mmj/1550480563.

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