Scientific Committee:
Organizing Committee:
Contact Information:
Denis Serbin email: dserbin
stevens.edu
phone: (201) 2165425

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Welcome to the First Online Seminar dedicated to Group Theory
and NonCommutative Algebra.
The seminar presents a unique opportunity for mathematicians from around the world to communicate and share their ideas on a regular basis without leaving the office or even home. Participants include faculty and students from US, Canada, Australia, Europe and Russia.
If you are a firsttime participant please
visit the technical advice page.
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Next Presentation 
Thursday, May 5, noon (New York Time) 
Oleg Bogopolski (HeinrichHeineUniversität Düsseldorf, Germany)
"From local to global conjugacy in relatively hyperbolic groups"
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Abstract:
Relatively hyperbolic groups were introduced by Gromov (1987). It is known (see Hrushka (2010)) that
essentially different definitions given by Gromov, Bowditch, and Osin coincide in the case, where
the ambient group is countable and the peripheral subgroups are infinite. In the first part of my talk
I will recall the combinatorial definition of Osin and formulate some statements which help to work in
this area. In the second part I will explain new results concerning the conjugacy of subgroups in relatively
hyperbolic groups. In particular, we prove the following theorem.
Theorem. Suppose that a finitely generated group G is hyperbolic relative to a collection
of subgroups P. Let H_{1}, H_{2} be subgroups of G such that H_{1} is relatively
quasiconvex with respect to P and H_{2} has a loxodromic element. Suppose that H_{2} is
elementwise conjugate into H_{1}. Then there exists a finite index subgroup of H_{2} which
is conjugate into H_{1}. The minimal length of the conjugator can be estimated.
Corollary. Let G be a limit group and let H_{1} and H_{2} be subgroups of G,
where H_{1} is finitely generated. Suppose that H_{2} is elementwise conjugate into H_{1}.
Then there exists a finite index subgroup of H_{2} which is conjugate into H_{1}.
The index depends only on H_{1}. The minimal length of the conjugator can be estimated. This implies that
limit groups are subgroup conjugacy separable.
Other theorems concerning hyperbolic virtually compact special groups will be given in the talk.
This is a joint work with K.U. Bux.

Seminar Schedule Spring 2016 

