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Displaying similar documents to “Growth tightness of free and amalgamated products”

Følner sequences in polycyclic groups.

Christophe Pittet (1995)

Revista Matemática Iberoamericana

Similarity:

The isoperimetric inequality |∂Ω| / |Ω| = constant / log |Ω| for finite subsets Ω in a finitely generated group Γ with exponential growth is optimal if Γ is polycyclic.

On exponential growth rates for free groups.

Malik Koubi (1998)

Publicacions Matemàtiques

Similarity:

Let F be a free group of rank p ≥ 2. It is well-known that, with respect to a p-element generating set, that is, a basis, the exponential growth rate of F is 2p-1. We show that the exponential growth rate τ of a group G with respect to a p-element generating set X is 2p-1 if and only if G is free on X; otherwise τ < 2p-1. We also prove that, for any finite generating set X of F which is disjoint from X, the exponential growth rate τ of F with respect to X is 2p-1 if and only if...

Conjugacy pinched and cyclically pinched one-relator groups.

Benjamin Fine, Gerhard Rosenberger, Michael Stille (1997)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

Here we consider two classes of torsion-free one-relator groups which have proved quite amenable to study-the cyclically pinched one-relator groups and the conjugacy pinched one-relator groups. The former is the class of groups which are free products of free groups with cyclic amalgamations while the latter is the class of HNN extensions of free groups with cyclic associated subgroups. Both are generalizations of surface groups. We compare and contrast results in these classes relative...

Free and non-free subgroups of the fundamental group of the Hawaiian Earrings

Andreas Zastrow (2003)

Open Mathematics

Similarity:

The space which is composed by embedding countably many circles in such a way into the plane that their radii are given by a null-sequence and that they all have a common tangent point is called “The Hawaiian Earrings”. The fundamental group of this space is known to be a subgroup of the inverse limit of the finitely generated free groups, and it is known to be not free. Within the recent move of trying to get hands on the algebraic invariants of non-tame (e.g. non-triangulable) spaces...