Small cancellations over relatively hyperbolic groups and embedding theorems
Small cancellations over relatively hyperbolic groups and embedding theorems
复制标题
相对双曲群和嵌入定理的小抵消
DOI：
10.4007/annals.2010.172.1
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发表时间：
2004
影响因子：
4.9
通讯作者：
D. Osin
中科院分区：
文献类型：
--
作者：
D. Osin
我们将普通双曲群上的小消去理论推广到相对双曲群上。这个推广，然后用来证明各种嵌入定理可数群。例如，我们证明了任何可数挠自由群都可以嵌入到一个具有两个共轭类的生成群中。特别是，这给出了肯定的答案，以著名的问题，存在一个非平凡生成群G的其他<$/2 <$，使所有的非平凡元素的G是共轭的。
We generalize the small cancellation theory over ordinary hyperbolic groups to relatively hyperbolic settings. This generalization is then used to prove various embedding theorems for countable groups. For instance, we show that any countable torsion free group can be embedded into a finitely generated group with exactly two conjugacy classes. In particular, this gives the affirmative answer to the well-known question of the existence of a finitely generated group G other than ℤ/2ℤ such that all nontrivial elements of G are conjugate.