## Abstract

The classification of p-groups of maximal class still is a wide open problem. Coclass Conjecture W proposes a way to approach such a classification: It suggests that the coclass graph G associated with the p-groups of maximal class can be determined from a finite subgraph using certain periodic patterns. Here we consider the subgraph G of G associated with those p-groups of maximal class whose automorphism group orders are divisible by p-1. We describe the broad structure of G by determining its so-called skeleton.We investigate the smallest interesting case p = 7 in more detail using computational tools, and propose an explicit version of Conjecture W for G for arbitrary p ≥ 7. Our results are the first explicit evidence in support of Conjecture W for a coclass graph of infinite width.

Original language | English |
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Pages (from-to) | 227-256 |

Number of pages | 30 |

Journal | Journal of Group Theory |

Volume | 20 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2017 |