We establish a general normal subgroup theorem for commensurators of lattices in locally compact groups. While the statement is completely elementary, its proof, which rests on the original strategy ofMargulis in the case of higher rank lattices, relies heavily on analytic tools pertaining to amenability and Kazhdan’s property (T). It is a counterpart to the normal subgroup theorem for irreducible lattices of Bader and the second named author, and may also be used to sharpen that result when one of the ambient factors is totally disconnected.
1
Vanderbilt University, Nashville, USA
2
Tel Aviv University, Israel
Darren Creutz; Yehuda Shalom. A normal subgroup theorem for commensurators of lattices. Groups, geometry, and dynamics, Tome 8 (2014) no. 3, pp. 789-810. doi: 10.4171/ggd/248
@article{10_4171_ggd_248,
author = {Darren Creutz and Yehuda Shalom},
title = {A normal subgroup theorem for commensurators of lattices},
journal = {Groups, geometry, and dynamics},
pages = {789--810},
year = {2014},
volume = {8},
number = {3},
doi = {10.4171/ggd/248},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/248/}
}
TY - JOUR
AU - Darren Creutz
AU - Yehuda Shalom
TI - A normal subgroup theorem for commensurators of lattices
JO - Groups, geometry, and dynamics
PY - 2014
SP - 789
EP - 810
VL - 8
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/248/
DO - 10.4171/ggd/248
ID - 10_4171_ggd_248
ER -
%0 Journal Article
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%A Yehuda Shalom
%T A normal subgroup theorem for commensurators of lattices
%J Groups, geometry, and dynamics
%D 2014
%P 789-810
%V 8
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/248/
%R 10.4171/ggd/248
%F 10_4171_ggd_248
