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Thursday, February 23, 2006

**Abstract:** Finding description of finitely generated groups acting freely on Lambda-trees, or, equivalently groups having free length functions in Lambda (where Lambda is an ordered abelian group) is one of the major problems in Geometric Group Theory. This problem was solved for some special cases of Lambda but still is far from being solved in the general case. In my talk, at first, I'm going to introduce a natural restriction on length function which is called the regularity condition. Then I'm going to present the description of finitely generated groups with regular free length functions in Z^n, and to discuss why regularity condition is important. This is a joint work with O. Kharlampovich, A. Myasnikov and V. Remeslennikov.