On Unipotent Radicals of Pseudo-Reductive Groups

Michael Bate, Benjamin Martin, Gerhard Röhrle, 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(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
Issue number2
Early online date18 Feb 2019
Publication statusPublished - 1 Jun 2019




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