Automorphism groups of right-angled buildings: simplicity and local splittings

Pierre-Emmanuel Caprace¹

¹ Université Catholique de Louvain, IRMP Chemin du Cyclotron 2 1348 Louvain-la-Neuve, Belgium

Fundamenta Mathematicae, Tome 224 (2014) no. 1, pp. 17-51

Résumé

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.

Détail

DOI : 10.4064/fm224-1-2

Keywords: group type preserving automorphisms irreducible semiregular thick right angled building abstractly simple building locally finite gives large family compactly generated abstractly simple locally compact groups specialising appropriate cases obtain examples simple groups locally indecomposable have locally normal subgroups decomposing non trivially direct products whose factors locally normal