Vol. 318, No. 1, 2022

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Generalized ideal classes in application to toroidal solenoids

Maria Sabitova

Vol. 318 (2022), No. 1, 189–228
DOI: 10.2140/pjm.2022.318.189

We study certain subgroups GA of n defined by nonsingular n × n-matrices A with integer coefficients. In the first nontrivial case when n = 2, we give necessary and sufficient conditions for two such groups to be isomorphic. Namely, in the generic case when the characteristic polynomial of A is irreducible, we attach a generalized ideal class to A and essentially, two groups are isomorphic if and only if the corresponding ideal classes are equivalent. The obtained results can be applied to studying associated toroidal solenoids.

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ideal classes, solenoids, odometers, matrices
Mathematical Subject Classification
Primary: 11Z05
Received: 25 June 2021
Revised: 11 November 2021
Accepted: 2 April 2022
Published: 1 August 2022
Maria Sabitova
Department of Mathematics
Queens College CUNY
Flushing, NY
United States