Uniform Growth in Groups of Exponential Growth
Uniform Growth in Groups of Exponential Growth
复制标题
指数增长组中的均匀增长
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
P. Harpe
中科院分区：
文献类型：
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作者：
P. Harpe
这是对具有一致指数增长的有限生成群的例子和类的阐述。主要的例子是非交换自由群、具有模不同于1的特征值的自由交换群的半直积，以及Golod-Shafarevich无限有限生成的p-群。这类群包括实际上具有非交换自由商的群、非初等双曲群、适当的合并自由积、HNN-扩张和1-相关群，以及指数增长的可解群。提出了几个有待解决的问题。
This is an exposition of examples and classes of finitely-generated groups which have uniform exponential growth. The main examples are non-Abelian free groups, semi-direct products of free Abelian groups with automorphisms having an eigenvalue of modulus distinct from 1, and Golod–Shafarevich infinite finitely-generated p-groups. The classes include groups which virtually have non-Abelian free quotients, nonelementary hyperbolic groups, appropriate free products with amalgamation, HNN-extensions and one-relator groups, as well as soluble groups of exponential growth. Several open problems are formulated.