The frame of the graph associated with the p-groups of maximal class
Group Theory
2025-12-15 v1
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.
Keywords
Cite
@article{arxiv.2512.11379,
title = {The frame of the graph associated with the p-groups of maximal class},
author = {Bettina Eick and Patali Komma and Subhrajyoti Saha},
journal= {arXiv preprint arXiv:2512.11379},
year = {2025}
}