On the classification of prime‐power groups by coclass
On the classification of prime‐power groups by coclass
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关于素幂群的共类分类
DOI：
10.1112/blms/bdn007
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发表时间：
2008
影响因子：
0.9
通讯作者：
C. Leedham
中科院分区：
文献类型：
--
作者：
B. Eick;C. Leedham
通过对纽曼和奥布莱恩的猜想P给出构造性证明，我们将上类r的某些p-群的分类归结为有限计算.对于p=2的情形，我们证明了上类r的所有2-群都可以通过许多参数表示来分类。猜想P的一个非构造性证明由du Sautoy使用zeta函数理论给出。我们的构造性证明使用同调代数。它为所考虑的p-群给出了更精确的结果和详细的结构定理。
By giving a constructive proof of Conjecture P of Newman and O’Brien, we reduce the classification of certain p‐groups of coclass r to a finite calculation. For the case p=2 we show that all 2‐groups of coclass r can be classified by finitely many parametrised presentations. A non‐constructive proof of Conjecture P was given by du Sautoy, using the theory of zeta functions. Our constructive proof uses homological algebra. It yields more precise results and detailed structure theorems for the p‐groups under consideration.