Year: 2025
Type: preprint
Abstract: We investigate the computability of the isomorphism set $\operatorname{Iso}(G_A,G_B)$ between $G_A$ and $G_B$, where $G_A$ is a subgroup of $\mathbb{Q}^n$ generated by columns of integer powers of a non-singular $n \times n$-matrix $A$ with integer entries. Assuming that the characteristic polynomial of $A$ is irreducible -- and under an additional condition when $n$ is not prime -- we prove that $\operatorname{Iso}(G_A,G_B)$ is computable; that is, there exists an algorithm that determines the structure in finitely many steps. We also present illustrative examples.
Source: arXiv (Cornell University)
Author: Sabitova, Maria
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7080136620
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