Small cancellations over relatively hyperbolic groups and embedding theorems
Annals of mathematics, Tome 172 (2010) no. 1, pp. 1-39
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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 $\mathbb Z/2\mathbb Z$ such that all nontrivial elements of $G$ are conjugate.
@article{10_4007_annals_2010_172_1,
author = {Denis Osin},
title = {Small cancellations over relatively hyperbolic groups and embedding theorems},
journal = {Annals of mathematics},
pages = {1--39},
publisher = {mathdoc},
volume = {172},
number = {1},
year = {2010},
doi = {10.4007/annals.2010.172.1},
mrnumber = {2680416},
zbl = {1203.20031},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.1/}
}
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%0 Journal Article %A Denis Osin %T Small cancellations over relatively hyperbolic groups and embedding theorems %J Annals of mathematics %D 2010 %P 1-39 %V 172 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.1/ %R 10.4007/annals.2010.172.1 %G en %F 10_4007_annals_2010_172_1
Denis Osin. Small cancellations over relatively hyperbolic groups and embedding theorems. Annals of mathematics, Tome 172 (2010) no. 1, pp. 1-39. doi: 10.4007/annals.2010.172.1
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