Description:
We 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 (G ̄k) 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