Sieve methods in group theory I: Powers in linear groups
Sieve methods in group theory I: Powers in linear groups
复制标题
群论中的筛法 I：线性群中的幂
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
C. Meiri
中科院分区：
文献类型：
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作者：
A. Lubotzky;C. Meiri
给出了一种一般的群筛法。它使人们能够“测量”一个随机生成的组的子集。作为一个应用，我们证明了如果Γ是一个特征为零的非虚可解线性群，则Γ的真幂集是指数小的.这是对[HKLS]主要成果的深远加强。
A general sieve method for groups is formulated. It enables one to “measure” subsets of a finitely generated group. As an application we show that if Γ is a finitely generated non virtually-solvable linear group of characteristic zero then the set of proper powers in Γ is exponentially small. This is a far reaching strengthening of the main result of [HKLS].