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arXiv · 2512.11379

The frame of the graph associated with the p-groups of maximal class

Bettina Eick·Patali Komma·Subhrajyoti Saha
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Abstract

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.

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Bettina Eick, Patali Komma, Subhrajyoti Saha. 2025-12-12. The frame of the graph associated with the p-groups of maximal class. https://arxiv.org/abs/2512.11379

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