This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Bate, MichaelMartin, BenjaminRöhrle, GerhardStewart, David I.2019-06-2820171864-7596https://doi.org/10.34657/2908https://oa.tib.eu/renate/handle/123456789/2665We establish some results on the structure of the geometric unipotent radicals of pseudo-reductive k-groups. In particular, 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′. We prove that the unipotent radical Ru(Gk¯) of the extension of scalars of G to the algebraic closure k¯ of k has exponent e. Our main theorem is to give bounds on the nilpotency class of geometric unipotent radicals of standard pseudo-reductive groups, which are sharp in many cases.application/pdfeng510Report