Geodesic
CHARACTERIZATIONS OF LOCALLY FINITE ACTIONS OF GROUPS ON SETS
Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 285-288

Voir la notice de l'article provenant de la source Cambridge University Press

We show that an action of a group on a set X is locally finite if and only if X is not equidecomposable with a proper subset of itself. As a consequence, a group is locally finite if and only if its uniform Roe algebra is finite. 
SCARPARO, EDUARDO. CHARACTERIZATIONS OF LOCALLY FINITE ACTIONS OF GROUPS ON SETS. Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 285-288. doi: 10.1017/S001708951700009X
@article{10_1017_S001708951700009X,
     author = {SCARPARO, EDUARDO},
     title = {CHARACTERIZATIONS {OF} {LOCALLY} {FINITE} {ACTIONS} {OF} {GROUPS} {ON} {SETS}},
     journal = {Glasgow mathematical journal},
     pages = {285--288},
     year = {2018},
     volume = {60},
     number = {2},
     doi = {10.1017/S001708951700009X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951700009X/}
}
TY  - JOUR
AU  - SCARPARO, EDUARDO
TI  - CHARACTERIZATIONS OF LOCALLY FINITE ACTIONS OF GROUPS ON SETS
JO  - Glasgow mathematical journal
PY  - 2018
SP  - 285
EP  - 288
VL  - 60
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708951700009X/
DO  - 10.1017/S001708951700009X
ID  - 10_1017_S001708951700009X
ER  - 
%0 Journal Article
%A SCARPARO, EDUARDO
%T CHARACTERIZATIONS OF LOCALLY FINITE ACTIONS OF GROUPS ON SETS
%J Glasgow mathematical journal
%D 2018
%P 285-288
%V 60
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708951700009X/
%R 10.1017/S001708951700009X
%F 10_1017_S001708951700009X

[1] 1. Glasner, Y. and Monod, N., Amenable actions, free products and a fixed point property, Bull. London Math. Soc. 39 (1) (2007), 138–150. Google Scholar

[2] 2. Juschenko, K. and Monod, N. Cantor systems, piecewise translations and simple amenable groups, Ann. Math. 178 (2) (2013), 775–787. Google Scholar

[3] 3. Kellerhals, J., Monod, N. and Rørdam, M., Non-supramenable groups acting on locally compact spaces, Doc. Math. 18(2013), 1597–1626. Google Scholar

[4] 4. Shalom, Y., Harmonic analysis, cohomology, and the large-scale geometry of amenable groups, Acta Mathematica 192 (2) (2004), 119–185. Google Scholar

[5] 5. Silva, P. V. and Soares, F., Howson's property for semidirect products of semilattices by groups, Commun. Algebra 44 (6) (2016), 2482–2494. Google Scholar

[6] 6. Wagon, S., The Banach–Tarski paradox, vol. 24 (Cambridge University Press, Cambridge, 1993). Google Scholar

[7] 7. Wei, S., On the quasidiagonality of Roe algebras, Sci. China Math. 54 (5) (2011), 1011–1018. Google Scholar

[8] 8. Żuk, A., On an isoperimetric inequality for infinite finitely generated groups, Topology 39 (5) (2000), 947–956. Google Scholar

Cité par Sources :