Year: 2025
Type: article
Abstract: In the paper of Duke and Hopkins (2005), following the approach of E.I. Zolotarev, an analogue of the quadratic reciprocity law for groups was obtained using the Kronecker symbol. We present a short proof of this statement using the Jacobi symbol. The work is mainly of a methodological nature. In this regard, we also provide a proof of the result established in the paper by Frobenius (1914), related to the combinatorial interpretation of the Jacobi symbol.
Author: A. N. Abyzov
Institution: Kazan Federal University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4410046919