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

Pierre-Emmanuel Caprace. "Automorphism groups of right-angled buildings: simplicity and local splittings." Fundamenta Mathematicae 224.1 (2014): 17-51. <http://eudml.org/doc/283266>.

@article{Pierre2014,
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.},
author = {Pierre-Emmanuel Caprace},
journal = {Fundamenta Mathematicae},
keywords = {simple groups; right-angled buildings; BN-pairs; locally compact groups; locally normal subgroups; right-angled Coxeter systems},
language = {eng},
number = {1},
pages = {17-51},
title = {Automorphism groups of right-angled buildings: simplicity and local splittings},
url = {http://eudml.org/doc/283266},
volume = {224},
year = {2014},
}

TY - JOUR
AU - Pierre-Emmanuel Caprace
TI - Automorphism groups of right-angled buildings: simplicity and local splittings
JO - Fundamenta Mathematicae
PY - 2014
VL - 224
IS - 1
SP - 17
EP - 51
AB - 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.
LA - eng
KW - simple groups; right-angled buildings; BN-pairs; locally compact groups; locally normal subgroups; right-angled Coxeter systems
UR - http://eudml.org/doc/283266
ER -