We show that the inert subgroups of the lamplighter group fall into exactly five commensurability classes. The result is then connected with the theory of totally disconnected locally compact groups and with algebraic entropy.
Castellano, I., Cook, G., Kropholler, P. (2020). A property of the lamplighter group. TOPOLOGICAL ALGEBRA AND ITS APPLICATIONS, 8(1), 1-4 [10.1515/taa-2020-0001].
A property of the lamplighter group
Castellano, I.
;
2020
Abstract
We show that the inert subgroups of the lamplighter group fall into exactly five commensurability classes. The result is then connected with the theory of totally disconnected locally compact groups and with algebraic entropy.
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