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In this chapter, we explore the coclass graphs (p, 1) for p ≥ 5 in greater depth, with a particular focus on a possible Periodicity II. More precisely, we consider the branches of the unique maximal coclass tree in (p, 1) and for each branch we introduce a partition of its skeleton into Galois trees. The main result of this chapter is a complete description of the Galois trees associated with the maximal Galois order.

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Groups of maximal class

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  • 发表日期：

    2026年

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  • Heiko Dietrich,
  • Bettina Eick

摘要

In this chapter, we explore the coclass graphs (p, 1) for p ≥ 5 in greater depth, with a particular focus on a possible Periodicity II. More precisely, we consider the branches of the unique maximal coclass tree in (p, 1) and for each branch we introduce a partition of its skeleton into Galois trees. The main result of this chapter is a complete description of the Galois trees associated with the maximal Galois order.