1Université Catholique de Louvain, Chemin du Cyclotron 2, Bte L7.01.02, 1348 Louvain-la-Neuve, Belgium 2School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia
Journal of Lie Theory, Tome 24 (2014) no. 4, pp. 957-967
The Tits core G+ of a totally disconnected locally compact group G is defined as the abstract subgroup generated by the closures of the contraction groups of all its elements. We show that a dense subgroup is normalised by the Tits core if and only if it contains it. It follows that every dense subnormal subgroup contains the Tits core. In particular, if G is topologically simple, then the Tits core is abstractly simple, and when G+ is non-trivial, it is the smallest dense normal subgroup. The proofs are based on the fact, of independent interest, that the map which associates to an element the closure of its contraction group is continuous.
Pierre-Emmanuel Caprace
1
;
Colin D. Reid
2
;
George A. Willis
2
1
Université Catholique de Louvain, Chemin du Cyclotron 2, Bte L7.01.02, 1348 Louvain-la-Neuve, Belgium
2
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia
Pierre-Emmanuel Caprace; Colin D. Reid; George A. Willis. Limits of Contraction Groups and the Tits Core. Journal of Lie Theory, Tome 24 (2014) no. 4, pp. 957-967. http://geodesic.mathdoc.fr/item/JOLT_2014_24_4_a2/
@article{JOLT_2014_24_4_a2,
author = {Pierre-Emmanuel Caprace and Colin D. Reid and George A. Willis},
title = {Limits of {Contraction} {Groups} and the {Tits} {Core}},
journal = {Journal of Lie Theory},
pages = {957--967},
year = {2014},
volume = {24},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2014_24_4_a2/}
}
TY - JOUR
AU - Pierre-Emmanuel Caprace
AU - Colin D. Reid
AU - George A. Willis
TI - Limits of Contraction Groups and the Tits Core
JO - Journal of Lie Theory
PY - 2014
SP - 957
EP - 967
VL - 24
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2014_24_4_a2/
ID - JOLT_2014_24_4_a2
ER -
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%P 957-967
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%F JOLT_2014_24_4_a2
