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.

18 pages