scholarly journals Asymptotic cones of HNN extensions and amalgamated products

2014 ◽  
Vol 14 (1) ◽  
pp. 551-595
Author(s):  
Curtis Kent
Keyword(s):  
Asymptotic Cones ◽  
Hnn Extensions ◽  
Amalgamated Products

Semistability of amalgamated products and HNN-extensions

1992 ◽  
Vol 98 (471) ◽  
pp. 0-0 ◽  
Author(s):  
Michael L. Mihalik ◽  
Steven T. Tschantz
Keyword(s):  
Hnn Extensions ◽  
Amalgamated Products

scholarly journals CSA-groups and separated free constructions

1995 ◽  
Vol 52 (1) ◽  
pp. 63-84 ◽  
Author(s):  
D. Gildenhuys ◽  
O. Kharlampovich ◽  
A. Myasnikov
Keyword(s):  
Abelian Subgroup ◽  
Dihedral Group ◽  
Hyperbolic Groups ◽  
Maximal Abelian Subgroup ◽  
Hnn Extensions ◽  
Abelian Subgroups ◽  
Amalgamated Products ◽  
Free Constructions ◽  
Torsion Free

A group G is called a CSA-group if all its maximal Abelian subgroups are malnormal; that is, Mx ∩ M = 1 for every maximal Abelian subgroup M and x ∈ G − M. The class of CSA-groups contains all torsion-free hyperbolic groups and all groups freely acting on λ-trees. We describe conditions under which HNN-extensions and amalgamated products of CSA-groups are again CSA. One-relator CSA-groups are characterised as follows: a torsion-free one-relator group is CSA if and only if it does not contain F2 × Z or one of the nonabelian metabelian Baumslag-Solitar groups B1, n = 〈x, y | yxy−1 = xn〉, n ∈ Z ∂ {0, 1}; a one-relator group with torsion is CSA if and only if it does not contain the infinite dihedral 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 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).

HIGH DIMENSIONAL KNOT GROUPS AND HNN EXTENSIONS OF THE FIBONACCI GROUPS

1998 ◽  
Vol 07 (04) ◽  
pp. 503-508 ◽  
Author(s):  
ANDRZEJ SZCZEPAŃSKI
Keyword(s):  
High Dimensional ◽  
New Class ◽  
Hnn Extensions

We shall present a new class of examples of high dimensional knot groups. All of them are HNN extensions of the Fibonacci groups. We give also some characterization of these groups.

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