Equations and fully residually free groups
نویسندگان
چکیده
Solving equations is one of the main themes in mathematics. A large part of the combinatorial group theory revolves around the word and conjugacy problems particular types of equations in groups. Whether a given equation has a solution in a given group is, as a rule, a non-trivial problem. A more general and more difficult problem is to decide which formulas of the first-order logic hold in a given group. Around 1945 A. Tarski put forward two problems on elementary theories of free groups that served as a motivation for much of the research in group theory and logic for the last sixty years. A joint effort of mathematicians of several generations culminated in the following theorems, solving these Tarski’s conjectures.
منابع مشابه
1 M ay 2 00 9 The fully residually F quotients of F ∗ 〈 x , y 〉
We describe the fully residually F groups; or limit groups relative to F ; that arise as the coordinate groups of irreducible systems of equations in two variables over a free group F that have coefficients in F. We use the structure theory of f.g. fully residually free groups and Bass-Serre theory. In particular we use foldings sequences for subgroups of fundamental groups of graphs of groups.
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