The Dade group of a p-group
The Dade group of a p-group
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p 群的 Dade 群
DOI：
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发表时间：
2006
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通讯作者：
S. Bouc
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作者：
S. Bouc
设p为素数。本文解决了自Dade于1978年（[19]，[20]）发表论文后公开的任意有限p-群P上的内置换模群D（P）的结构问题，并证明了[4]，[10]中的结论.这导致了D（P）的显式生成元和显式关系的表示，推广了Dade在P是阿贝尔时得到的表示。一个独立感兴趣的关键结果是从伯恩赛德群到有理特征标群的自然映射的核的显式描述，根据阶为p3的超特殊群和指数p（如果p ≥ 2），或者如果p=2，则为至少8阶的所有二面体群。
Let p be a prime number. This paper solves the question of the structure of the group D(P) of endo-permutation modules over an arbitrary finite p-group P, that was open after Dade’s original papers in 1978 ([19], [20]), and it gives a proof of the conjectures proposed in [4] and [10]. This leads to a presentation of D(P) by explicit generators and relations, generalizing the presentation obtained by Dade when P is abelian.A key result of independent interest is the explicit description of the kernel of the natural map from the Burnside group to the group of rational characters, in terms of the extraspecial group of order p3 and exponent p if p≠2, or of all dihedral groups of order at least 8 if p=2.