Totally disconnected locally compact groups locally of finite rank
(2015) Cambridge Philosophical Society. Mathematical Proceedings — Vol. 158, n° 3, p. 505-530 (2015)
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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.
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Wesolek, P. (2015). Totally disconnected locally compact groups locally of finite rank. Cambridge Philosophical Society. Mathematical Proceedings, 158(3), 505-530. https://doi.org/10.1017/S0305004115000122 (Original work published 2015)