[Turkmath:8370] Istanbul Bilgi University Departmental Seminar May 11

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Dear All,

Krzysztof Krupinski (Uniwersytet Wroclawski) will give a talk at our
departmental seminar on Friday (May 11) at 16:00 in the room D-135.
The title and abstract below.

Best,

Piotr-------------------------------------------------------------------------------
Title: On omega-categorical groups and rings with some model-theoretic properties

Abstract: A general motivation is to understand the structure of 
omega-categorical groups and rings satisfying various natural 
model-theoretic assumptions.

There is a long history of results of this kind. The fundamental theorem 
of Baur, Cherlin and Macintyre says that omega-categorical, stable groups 
are nilpotent-by-finite. A long-standing conjecture states that they are 
even abelian-by-finite, which is known to be true in the superstable case. 
As to the omega-categorical, stable rings, they are nilpotent-by-finite, 
and it is conjectured that they are null-by-finite. As for groups, this 
conjecture is known to be true in the superstable case.

There are many generalizations and variants of these results. For example, 
omega-categorical groups with  NSOP (the negation of the strict order 
property) are nilpotent-by-finite, and omega-categorical rings with  NSOP 
are nilpotent-by-finite, too.
%It is also known that omega-categorical, supersimple groups are 
finite-by-abelian-by-finite, and omega-categorical, supersimple rings are 
finite-by-null-by-finite.

In one of my papers, I was considering omega-categorical groups and rings 
with NIP, proving, for example, that each omega-categorical ring with NIP 
is nilpotent-by-finite. In the recent two joint papers with Jan 
Dobrowolski, we have been investigating the structure of 
omega-categorical, generically stable groups and rings, proving that they 
are nilpotent-by-finite. During the lecture, I will discuss the main 
results from these three papers.

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Özge ÜLKEM

 		 	   		  
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