On the Classification of Perfect Prishchepov Groups
Abstract
The Prishchepov groups $P(r,n,k,s,q)$ form a broad class of cyclically presented groups. We verify a conjectural characterisation of the perfect groups in this family. We first prove the conjecture for the case $\gcd(n,6)=1$ and then establish further cases beyond this coprimality condition. Consequently, we obtain a classification of perfect Prishchepov groups in a broad range of parameters.
Fields of Study & Subjects
Geometric and Algebraic Topology
Finite Group Theory Research
Mathematics and Applications
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 7 February 2026
- Language
- EN
- Document type
- Preprint