A topological equivalence relation for finitely presented groups
نویسندگان
چکیده
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 ...
متن کاملA Characterisation of Large Finitely Presented Groups
In this paper, we will consider finitely presented groups that have a finite index subgroup which admits a surjective homomorphism onto a non-abelian free group. Gromov called these groups large [4]. Large groups have particularly nice properties (for example, super-exponential subgroup growth). They also play an important rôle in lowdimensional topology: it is a major conjecture that the funda...
متن کاملJsj-splittings for Finitely Presented Groups over Slender Groups
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...
متن کاملFinitely generated nilpotent groups are finitely presented and residually finite
Definition 1. Let G be a group. G is said to be residually finite if the intersection of all normal subgroups of G of finite index in G is trivial. For a survey of results on residual finiteness and related properties, see Mag-nus, Karrass, and Solitar [6, Section 6.5]. We shall present a proof of the following well known theorem, which is important for Kharlampovich [4, 5]. See also O. V. Bele...
متن کاملDecompositions of finitely generated and finitely presented groups
In this paper we discuss the splitting or decomposing of finitely generated groups into free products, free products with amalgamation or HNN extensions and we discuss the JSJ decomposition of finitely presented groups.
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: Journal of Pure and Applied Algebra
سال: 2020
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2019.106300