On the Classification of Perfect Prishchepov Groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908819063308288 |
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| author | Sorkatti, Layla Chinyere, Ihechukwu |
| author_facet | Sorkatti, Layla Chinyere, Ihechukwu |
| contents | We study the Prishchepov groups $P(r,n,k,s,q)$, a unifying family of cyclically presented groups that encompasses many classical cases. For $n$ coprime to $6$, we prove a conjecture essentially characterizing when these groups are perfect: namely, $n$ divides either $2(k-1)-q$ (if $r \geq s$) or $q(r+s)$. This settles the classification of perfect Prishchepov groups under the co-primality condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07346 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Classification of Perfect Prishchepov Groups Sorkatti, Layla Chinyere, Ihechukwu Group Theory We study the Prishchepov groups $P(r,n,k,s,q)$, a unifying family of cyclically presented groups that encompasses many classical cases. For $n$ coprime to $6$, we prove a conjecture essentially characterizing when these groups are perfect: namely, $n$ divides either $2(k-1)-q$ (if $r \geq s$) or $q(r+s)$. This settles the classification of perfect Prishchepov groups under the co-primality condition. |
| title | On the Classification of Perfect Prishchepov Groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2602.07346 |