THE ZERO-IN-THE-SPECTRUM CONJECTURE AND FINITELY PRESENTED GROUPS
THE ZERO-IN-THE-SPECTRUM CONJECTURE AND FINITELY PRESENTED GROUPS
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谱中零猜想和有限群
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
Shin
中科院分区：
文献类型：
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作者：
Shin
本文介绍了一个算法，它把一个离散群G变换成另一个具有某些特殊性质的群G_n。例如，当G是一个不服从群时，则G不满足谱中零猜想的代数版本。此外，当G是n-生成的自由群时，G也是n-生成的，并且G的p-次群同调对所有p ≥ 3都有无穷秩.
We introduce an algorithm which transforms a discrete group G into another one GΨ which has some particular properties. For example when G is a nonamenable group, then GΨ does not satisfy an algebraic version of the zero-in-thespectrum conjecture. Moreover when G is a finitely generated free group, then GΨ is also finitely presented and the p-th group homology of GΨ have infinite rank for all p ≥ 3.