EXPONENTIALLY GENERIC SUBSETS OF GROUPS
EXPONENTIALLY GENERIC SUBSETS OF GROUPS
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DOI：
10.1215/ijm/1299679753
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发表时间：
2010-03-01
影响因子：
0.6
通讯作者：
Osin, Denis
中科院分区：
文献类型：
--
作者：
Gilman, Robert;Miasnikov, Alexei;Osin, Denis
在本文中，我们研究了泛型，即，典型的，行为的双曲群的生成子群，也是一般的行为的字的问题，顺从的群体。我们证明了一个非初等字双曲群的随机元素集很可能是一个很好嵌入的自由子群的一组自由生成元。我们还展示了一些提出的顺从的群体，其中的限制的字的问题是无法解决的每一个足够大的子集的话。
In this paper, we study the generic, i.e., typical, behavior of finitely generated subgroups of hyperbolic groups and also the generic behavior of the word problem for amenable groups. We show that a random set of elements of a nonelementary word hyperbolic group is very likely to be a set of free generators for a nicely embedded free subgroup. We also exhibit some finitely presented amenable groups for which the restriction of the word problem is unsolvable on every sufficiently large subset of words.