On unipotent radicals of pseudo-reductive groups

2017/04/14 by Bate, Michael, Martin, Benjamin, Roehrle, Gerhard +1
#20G15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1704.04385

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 _k) of the extension of scalars of G to the algebraic closure k of k.

Related

• The Subgroup Structure of Pseudo-Reductive Groups
• On geometry of some pseudo-reductive groups
• The subgroup structure of pseudo-reductive groups
• Unipotent Generators for Arithmetic Groups
• Abelian Unipotent Subgroups of Reductive Groups