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.

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