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Abstract
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In 2000, Marc Burger and Shahar Mozes introduced universal groups acting on trees.
Such groups provide interesting examples of totally disconnected locally compact
groups. Intuitively, these are the largest groups for which all local actions satisfy a
prescribed behavior.
Since then, their study has evolved in various directions. In particular, Adrien
Le Boudec has studied
restricted universal groups, where the prescribed
behavior is allowed to be violated in a finite number of vertices. On the
other hand, we have been studying universal groups acting on
right-angled
buildings, a class of geometric objects with a much more general structure than
trees.
The aim of the current paper is to combine both ideas: we will study restricted
universal groups acting on right-angled buildings. We show several permutational and
topological properties of those groups, with, as a main result, a precise criterion for
when these groups are virtually simple.
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Keywords
right-angled buildings, universal groups, locally compact
groups, simple groups
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Mathematical Subject Classification
Primary: 22D05, 22F50, 51E24
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Milestones
Received: 25 July 2022
Revised: 22 December 2022
Accepted: 24 January 2023
Published: 13 September 2023
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