Unipotent normal subgroups of algebraic groups

2024/04/18 by Sercombe, Damian
#20G15 (Primary) 20G07 (Secondary) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2404.12221

Abstract

Let G be an affine algebraic group scheme over a field k. We show there exists a unipotent normal subgroup of G which contains all other such subgroups; we call it the restricted unipotent radical Rad_u(G) of G. We investigate some properties of Rad_u(G), and study those G for which Rad_u(G) is trivial. In particular, we relate these notions to their well-known analogues for smooth connected affine k-groups.

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