Automorphism groups of right-angled buildings: simplicity and local splittings
Volume 224 / 2014
Fundamenta Mathematicae 224 (2014), 17-51
MSC: 20E42, 22D05, 20E08, 20F65.
DOI: 10.4064/fm224-1-2
Abstract
We show that the group of type-preserving automorphisms of any irreducible semiregular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated abstractly simple locally compact groups. Specialising to appropriate cases, we obtain examples of such simple groups that are locally indecomposable, but have locally normal subgroups decomposing non-trivially as direct products, all of whose factors are locally normal.
