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arXiv · 1412.4800

The kernel of the adjoint representation of a p-adic Lie group need not have an abelian open normal subgroup

Helge Glockner
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Abstract

Let G be a p-adic Lie group and Ad be the adjoint representation of G on its Lie algebra. It was claimed in the literature that the kernel K of Ad always has an abelian open normal subgroup. We show by means of a counterexample that this assertion is false; it can even happen that K=G but G has no abelian subnormal subgroup except for the trivial group. The arguments are based on auxiliary results on subgroups of free products with central amalgamation.

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Helge Glockner. 2014-12-15. The kernel of the adjoint representation of a p-adic Lie group need not have an abelian open normal subgroup. https://arxiv.org/abs/1412.4800

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