Submission date: 5 March 2022

Abstract:

A decomposition of definable groups G in o-minimal structures inspired by the Jordan-Chevalley decomposition of linear algebraic groups is presented. As a consequence, we give a description of the commutator subgroup and show that when G has definable Levi subgroups, then [G, G] is definable. Along the way, we study disconnected groups, definable p-groups and 0-groups, abstractly compact subgroups, and give a few other structure decompositions.

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Full text arXiv 2203.02637: pdf, ps.