On the Classification of Perfect Prishchepov Groups

2026/02/28 by Layla Sorkatti, Ihechukwu Chinyere
Mathematics · #math.GR

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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.

Citations

• Cyclically presented groups as Labelled Oriented Graph groups
• Generalized Fibonacci groups H(r,n,s) that are connected Labelled\n Oriented Graph groups

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