On a theorem of Avez

Publication Type:
Journal Article
Journal of Group Theory, 2019, 22 (3), pp. 383 - 395
Issue Date:
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© de Gruyter 2019. For each symmetric, aperiodic probability measure on a finitely generated group G, we define a subset A consisting of group elements g for which the limit of the ratio n.g/=n.e/ tends to 1. We prove that A is a subgroup, is amenable, contains every finite normal subgroup, and G D A if and only if G is amenable. For non-amenable groups we show that A is not always a normal subgroup and can depend on the measure. We formulate some conjectures relating A to the amenable radical.
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