### 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 |

### Cite this

*Journal of Group Theory*,

*20*(2), 227-256. https://doi.org/10.1515/jgth-2016-0036

}

*Journal of Group Theory*, vol. 20, no. 2, pp. 227-256. https://doi.org/10.1515/jgth-2016-0036

**Finite p-groups of maximal class with 'large' automorphism groups.** / Dietrich, Heiko; Eick, Bettina.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Finite p-groups of maximal class with 'large' automorphism groups

AU - Dietrich, Heiko

AU - Eick, Bettina

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85014602237&partnerID=8YFLogxK

U2 - 10.1515/jgth-2016-0036

DO - 10.1515/jgth-2016-0036

M3 - Article

VL - 20

SP - 227

EP - 256

JO - Journal of Group Theory

JF - Journal of Group Theory

SN - 1433-5883

IS - 2

ER -