scholarly journals Relative Dehn functions of amalgamated products and HNN-extensions

2006 ◽  
pp. 209-220 ◽  
Author(s):  
D. V. Osin
Keyword(s):  
Dehn Functions ◽  
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 Annular Dehn functions of groups

1998 ◽  
Vol 58 (3) ◽  
pp. 453-464 ◽  
Author(s):  
Stephen G. Brick ◽  
Jon M. Corson
Keyword(s):  
Conjugacy Problem ◽  
Upper Bounds ◽  
Dehn Function ◽  
Free Products ◽  
Dehn Functions ◽  
Finitely Presented Group ◽  
Hnn Extensions ◽  
Finite Subgroups ◽  
Boundary Curves ◽  
Finitely Presented

For a finite presentation of a group, or more generally, a two-complex, we define a function analogous to the Dehn function that we call the annular Dehn function. This function measures the combinatorial area of maps of annuli into the complex as a function of the lengths of the boundary curves. A finitely presented group has solvable conjugacy problem if and only if its annular Dehn function is recursive.As with standard Dehn functions, the annular Dehn function may change with change of presentation. We prove that the type of function obtained is preserved by change of presentation. Further we obtain upper bounds for the annular Dehn functions of free products and, more generally, amalgamations or HNN extensions over finite subgroups.

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 Second order Dehn functions and HNN-extensions

1999 ◽  
Vol 67 (2) ◽  
pp. 272-288 ◽  
Author(s):  
X. Wang ◽  
S. J. Pride
Keyword(s):  
Lower Bounds ◽  
Infinite Number ◽  
Second Order ◽  
Upper And Lower Bounds ◽  
Dehn Functions ◽  
Open Questions ◽  
Hnn Extensions

AbstractIn previous work [2] calculations of subquadratic second order Dehn functions for various groups were carried out. In this paper we obtain estimates for upper and lower bounds of second order Dehn functions of HNN-extensions, and use these to exhibit an infinite number of different superquadratic second order Dehn functions. At the end of the paper several open questions concerning second order Dehn functions of groups are discussed.

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