Generalized ideal classes in application to toroidal solenoids

We study certain subgroups $G_{A}$ of $ℚ^{n}$ defined by nonsingular $n \times n$ -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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Keywords

ideal classes, solenoids, odometers, matrices

Mathematical Subject Classification

Primary: 11Z05

Milestones

Received: 25 June 2021

Revised: 11 November 2021

Accepted: 2 April 2022

Published: 1 August 2022

Authors

Maria Sabitova
Department of Mathematics Queens College CUNY Flushing, NY United States

Vol. 318, No. 1, 2022

Maria Sabitova

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors