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The groups on the mainline of a maximal coclass tree T in a graph (p, r) can be determined as quotients S/γi (S) of the infinite pro-p-group ( associated with T . In this chapter we describe a method to construct groups in T that are not on the mainline. For large enough j , these groups form a subtree (the skeleton) Sj of the branch ẞj in T ; this subtree has the same root as ẞj .

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The skeletons of a coclass tree

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  • 发表日期：

    2026年

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  • Heiko Dietrich,
  • Bettina Eick

摘要

The groups on the mainline of a maximal coclass tree T in a graph (p, r) can be determined as quotients S/γi (S) of the infinite pro-p-group ( associated with T . In this chapter we describe a method to construct groups in T that are not on the mainline. For large enough j , these groups form a subtree (the skeleton) Sj of the branch ẞj in T ; this subtree has the same root as ẞj .