منابع مشابه
Finitely Presented Residually Free Groups
We establish a general criterion for the finite presentability of subdirect products of groups and use this to characterize finitely presented residually free groups. We prove that, for all n ∈ N, a residually free group is of type FPn if and only if it is of type Fn. New families of subdirect products of free groups are constructed, including the first examples of finitely presented subgroups ...
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We consider the family of irreducible cyclically presented groups on n generators whose generating word (in the standard rewrite) has length at most 15. Using the software packages KBMAG, quotpic and Magma, together with group and number theoretic methods, we show that if 6 ≤ n ≤ 100 then the group is non-trivial. In an appendix we list the 47 cases within 2 ≤ n ≤ 100 for which we know the grou...
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We construct an embedding of a free Burnside group B(m, n) of odd n > 2 and rank m > 1 in a finitely presented group with some special properties. The main application of this embedding is an easy construction of finitely presented non-amenable groups without noncyclic free subgroups (which provides a finitely presented counterexample to the von Neumann problem on amenable groups). As another a...
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We generalize the JSJ-splitting of Rips and Sela to give decompositions of nitely presented groups which capture splittings over certain classes of small subgroups. Such classes include the class of all 2-ended groups and the class of all virtually ZZ groups. The approach, called \track zipping", is relatively elementary, and diiers from the Rips-Sela approach in that it does not rely on the th...
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ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2007
ISSN: 1661-7207
DOI: 10.4171/ggd/3