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

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DOI

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
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     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/}
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