Year: 2026
Type: preprint
Abstract: This paper explores the failure of induction from all proper subgroups to generate the full representation ring, measured by a quotient group $Q_k(G)$. We extend existing results for cyclic groups to all finite abelian groups and calculate this quotient for all finite groups over fields of characteristic 0 by reducing to the abelian case. We briefly discuss extensions to positive characteristics via modular representation theory. Finally, we detail our result for certain well-known families of groups.
Source: arXiv (Cornell University)
Author: Dimmock, Sean
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223792460