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Totally disconnected locally compact groups locally of finite rank

Published online by Cambridge University Press:  13 March 2015

PHILLIP WESOLEK
PHILLIP WESOLEK*
Affiliation:
Université catholique de Louvain, Louvain-la-Neuve, Belgium. e-mail: [email protected]
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Abstract

We study totally disconnected locally compact second countable (t.d.l.c.s.c.) groups that contain a compact open subgroup with finite rank. We show such groups that additionally admit a pro-π compact open subgroup for some finite set of primes π are virtually an extension of a finite direct product of topologically simple groups by an elementary group. This result, in particular, applies to l.c.s.c. p-adic Lie groups. We go on to obtain a decomposition result for all t.d.l.c.s.c. groups containing a compact open subgroup with finite rank. In the course of proving these theorems, we demonstrate independently interesting structure results for t.d.l.c.s.c. groups with a compact open pro-nilpotent subgroup and for topologically simple l.c.s.c. p-adic Lie groups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 158 , Issue 3 , May 2015 , pp. 505 - 530
Copyright
Copyright © Cambridge Philosophical Society 2015 

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