The frame of the graph associated with the p-groups of maximal class
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917141698052096 |
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| author | Eick, Bettina Komma, Patali Saha, Subhrajyoti |
| author_facet | Eick, Bettina Komma, Patali Saha, Subhrajyoti |
| contents | The graph G(p) associated with the p-groups of maximal class is a major tool in their classification. We introduce a subgraph of the graph G(p) called its frame. Its construction is based on the Lazard correspondence. We show that every p-group of maximal class has a normal subgroup of order at most p whose quotient is in the frame. Since the frame is close to the full graph, it offers a new approach towards the classification of the p-groups of maximal class. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_11379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The frame of the graph associated with the p-groups of maximal class Eick, Bettina Komma, Patali Saha, Subhrajyoti Group Theory The graph G(p) associated with the p-groups of maximal class is a major tool in their classification. We introduce a subgraph of the graph G(p) called its frame. Its construction is based on the Lazard correspondence. We show that every p-group of maximal class has a normal subgroup of order at most p whose quotient is in the frame. Since the frame is close to the full graph, it offers a new approach towards the classification of the p-groups of maximal class. |
| title | The frame of the graph associated with the p-groups of maximal class |
| topic | Group Theory |
| url | https://arxiv.org/abs/2512.11379 |