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

Source abstract

The graph G ( p ) \mathcal {G}(p) associated with the p p -groups of maximal class is a major tool in their classification. We introduce a subgraph of G ( p ) \mathcal {G}(p) called its frame . Its construction is based on the Lazard correspondence. We show that every p p -group of maximal class has a normal subgroup of order at most p 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 these groups.