scholarly journals Rank Gradient andp-gradient of Amalgamated Free Products and HNN Extensions

2015 ◽  
Vol 43 (10) ◽  
pp. 4515-4527 ◽  
Author(s):  
Nathaniel Pappas
Keyword(s):  
Free Products ◽  
Amalgamated Free Products ◽  
Hnn Extensions ◽  
Rank Gradient

scholarly journals Separating conjugates in amalgamated free products and HNN extensions

1980 ◽  
Vol 29 (1) ◽  
pp. 35-51 ◽  
Author(s):  
Joan L. Dyer
Keyword(s):  
Nilpotent Groups ◽  
Conjugacy Classes ◽  
Free Products ◽  
Amalgamated Free Products ◽  
Hnn Extensions ◽  
Nontrivial Center ◽  
One Relator Groups ◽  
Amalgamated Subgroup ◽  
Conjugacy Separable ◽  
Base Group

AbstractA group G is termed conjugacy separable (c.s.) if any pair of distinct conjugacy classes may be mapped to distinct conjugacy classes in some finite epimorph of G. The free product of A and B with cyclic amalgamated subgroup H is shown to be c.s. if A and B are both free, or are both finitely generated nilpotent groups. Further, one-relator groups with nontrivial center and HNN extensions with c.s. base group and finite associated subgroups are also c.s.

scholarly journals C*-SIMPLE GROUPS: AMALGAMATED FREE PRODUCTS, HNN EXTENSIONS, AND FUNDAMENTAL GROUPS OF 3-MANIFOLDS

2011 ◽  
Vol 03 (04) ◽  
pp. 451-489 ◽  
Author(s):  
PIERRE DE LA HARPE ◽  
JEAN-PHILIPPE PRÉAUX
Keyword(s):  
Sufficient Conditions ◽  
Simple Groups ◽  
Fundamental Groups ◽  
Normal Subgroups ◽  
Free Products ◽  
Amalgamated Free Products ◽  
Hnn Extensions ◽  
Groups Acting On Trees ◽  
Jsj Decompositions ◽  
Fixed Point Sets

We establish sufficient conditions for the C*-simplicity of two classes of groups. The first class is that of groups acting on trees, such as amalgamated free products, HNN-extensions, and their nontrivial subnormal subgroups; for example normal subgroups of Baumslag–Solitar groups. The second class is that of fundamental groups of compact 3-manifolds, related to the first class by their Kneser–Milnor and JSJ decompositions. Much of our analysis deals with conditions on an action of a group Γ on a tree T which imply the following three properties: abundance of hyperbolic elements, better called strong hyperbolicity, minimality, both on the tree T and on its boundary ∂T, and faithfulness in a strong sense. An important step in this analysis is to identify automorphisms of T which are slender, namely such that their fixed-point sets in ∂T are nowhere dense for the shadow topology.

scholarly journals The growth of certain amalgamated free products and HNN-extensions

1992 ◽  
Vol 52 (3) ◽  
pp. 285-298 ◽  
Author(s):  
M. Edjvet ◽  
D. L. Johnson
Keyword(s):  
Rational Function ◽  
Normal Forms ◽  
Free Products ◽  
Growth Series ◽  
Amalgamated Free Products ◽  
Hnn Extensions ◽  
Rewrite Rules ◽  
Image Position

AbstractHere we mean growth in the sense of Milnor and Gromov. After a brief survey of known results, we compute the growth series of the groups, with respect to generators {x, y}. This is done using minimal normal forms obtained by informal use of judiciously chosen rewrite rules. In both of these examples the growth series is a rational function, and we suspect that this is not the case for the Baumslag-Solitar group.

scholarly journals RATIONAL SUBSETS IN HNN-EXTENSIONS AND AMALGAMATED PRODUCTS

2008 ◽  
Vol 18 (01) ◽  
pp. 111-163 ◽  
Author(s):  
MARKUS LOHREY ◽  
GÉRAUD SÉNIZERGUES
Keyword(s):  
Structural Properties ◽  
Finitely Generated ◽  
Free Products ◽  
Amalgamated Free Products ◽  
Hnn Extensions ◽  
Amalgamated Products

Several transfer results for rational subsets and finitely generated subgroups of HNN-extensions G = 〈 H,t; t-1 at = φ(a) (a ∈ A) 〉 and amalgamated free products G = H *A J such that the associated subgroup A is finite. These transfer results allow to transfer decidability properties or structural properties from the subgroup H (resp. the subgroups H and J) to the group G.

scholarly journals Relation modules of amalgamated free products and HNN extensions

1989 ◽  
Vol 31 (3) ◽  
pp. 263-270 ◽  
Author(s):  
Torsten Hannebauer
Keyword(s):  
Normal Subgroup ◽  
Exact Sequence ◽  
Short Exact Sequence ◽  
Free Products ◽  
Relation Module ◽  
Amalgamated Free Products ◽  
Hnn Extensions ◽  
Image Position

Let G be a group anda free presentation of G, i.e. a short exact sequence of groups with F free. Conjugation in F induces on = R/R', the abelianized normal subgroup R, the structure of a right G-module (if r∈ R, x∈ F then (r)(xπ) = x-1rxR'). The G-module is called the relation module determined by the presentation (1). For a detailed discussion of this subject we refer to Gruenberg [3].

scholarly journals The residual finiteness of HNN-extensions and generalized free products of nilpotent groups: a characterization

1992 ◽  
Vol 53 (3) ◽  
pp. 408-420 ◽  
Author(s):  
E. Raptis ◽  
D. Varsos
Keyword(s):  
Nilpotent Groups ◽  
Residual Finiteness ◽  
Finitely Generated ◽  
Free Products ◽  
Hnn Extensions ◽  
Base Group ◽  
Generalized Free Products

AbstractWe study the residual finiteness of free products with amalgamations and HNN-extensions of finitely generated nilpotent groups. We give a characterization in terms of certain conditions satisfied by the associated subgroups. In particular the residual finiteness of these groups implies the possibility of extending the isomorphism of the associated subgroups to an isomorphism of their isolated closures in suitable overgroups of the factors (or the base group in case of HNN-extensions).

scholarly journals ON THE GROWTH OF GROUPS AND AUTOMORPHISMS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 869-874 ◽  
Author(s):  
MARTIN R. BRIDSON
Keyword(s):  
Finitely Generated ◽  
Free Products ◽  
Dehn Functions ◽  
Amalgamated Free Products ◽  
Growth Functions ◽  
Growth Of Groups

We consider the growth functions βΓ(n) of amalgamated free products Γ = A *C B, where A ≅ B are finitely generated, C is free abelian and |A/C| = |A/B| = 2. For every d ∈ ℕ there exist examples with βΓ(n) ≃ nd+1βA(n). There also exist examples with βΓ(n) ≃ en. Similar behavior is exhibited among Dehn functions.

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