On Two Variable Equations in Free Groups
نویسندگان
چکیده
منابع مشابه
One Variable Equations in Free Groups via Context Free Languages
We use context free languages to analyze solution sets to one variable equations over free groups.
متن کاملOne Variable Equations in Torsion-free Hyperbolic Groups
Let Γ be a torsion-free hyperbolic group. We show that the set of solutions of any system of equations with one variable in Γ is a finite union of points and cosets of centralizers if and only if any two-generator subgroup of Γ is free.
متن کاملOn the coordinate groups of irreducible systems of equations in two variables over free groups
We describe the fully residually F groups; or limit groups relative to F ; that arise from systems of equations in two variables over a free group F that have coefficients in F .
متن کاملTwo-Variable Word Equations
We consider languages expressed by word equations in two variables and give a complete characterization for their complexity functions, that is, the functions that give the number of words of the same length. Speci cally, we prove that there are only ve types of complexities: constant, linear, exponential, and two in between constant and linear. For the latter two, we give precise characterizat...
متن کاملSolving equations in free nilpotent groups
In this paper we show that any system of equations over a free nilpotent group of class c is either unitary or nullary. In fact, such a system either has a most general solution (akin to the most general solution of a system of linear diophantine equations), or every solution has a proper generalization. In principle we provide an algorithm for determining whether or not a most general solution...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1969
ISSN: 0002-9939
DOI: 10.2307/2036887