منابع مشابه
Equations and fully residually free groups
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 g...
متن کاملSubgroup Properties of Fully Residually Free Groups
We prove that fully residually free groups have the Howson property, that is the intersection of any two finitely generated subgroups in such a group is again finitely generated. We also establish some commensurability properties for finitely generated fully residually free groups which are similar to those of free groups. Finally we prove that for a finitely generated fully residually free gro...
متن کاملIsomorphism Problem for Finitely Generated Fully Residually Free Groups
We prove that the isomorphism problem for finitely generated fully residually free groups (or F-groups for short) is decidable. We also show that each F-group G has a decomposition that is invariant under automorphisms of G, and obtain a structure theorem for the group of outer automorphisms Out(G).
متن کاملFinite Index Subgroups of Fully Residually Free Groups
Using graph-theoretic techniques for f.g. subgroups of F we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked effectively. Also we obtain an analogue of Greenberg-Stallings Theorem for f.g. fully residually free groups, and prove that a f.g. non-abelian subgroup of a f.g. fully residually fre...
متن کاملAspherical fully residually free Kähler groups are Fuchsian
In this note, we prove that an aspherical fully residually free Kähler group is Fuchsian. One instances of this shows that cocompact lattices in PU(1, n) for n > 1 cannot be residually free. The proof uses some recent work of Delzant and Gromov.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2010
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2010.04.019