Automorphism groups and the isomorphism problem for frame 𝑝-groups of maximal class

Abstract The classification of 𝑝-groups of maximal class is a deep and long-standing problem in group theory. Recently, a new approach was introduced by Eick, Komma and Saha: this uses the Lazard correspondence to construct the so-called frame 𝑝-groups . The set of all frame 𝑝-groups forms a significant, but still controllable part of the set of all 𝑝-groups of maximal class and hence seems a good basis for a classification. This paper investigates the automorphism groups and the isomorphism problem for frame 𝑝-groups.