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218
RATIONAL SUBSETS IN HNNEXTENSIONS AND AMALGAMATED PRODUCTS
"... Several transfer results for rational subsets and finitely generated subgroups of HNNextensions 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 pr ..."
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Cited by 4 (3 self)
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Several transfer results for rational subsets and finitely generated subgroups of HNNextensions 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
Theories of HNNextensions and amalgamated products
 Proceedings of the 33st International Colloquium on Automata, Languages and Programming (ICALP 2006), Venice (Italy), number 4052 in Lecture Notes in Computer Science
, 2006
"... Abstract. It is shown that the existential theory of G with rational constraints, over an HNNextension G = 〈H, t; t −1 at = ϕ(a)(a ∈ A) 〉 is decidable, provided that the same problem is decidable in the base group H and that A is a finite group. The positive theory of G is decidable, provided that ..."
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Cited by 7 (4 self)
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Abstract. It is shown that the existential theory of G with rational constraints, over an HNNextension G = 〈H, t; t −1 at = ϕ(a)(a ∈ A) 〉 is decidable, provided that the same problem is decidable in the base group H and that A is a finite group. The positive theory of G is decidable, provided
Equations in HNNextensions
, 2006
"... Abstract. Let H be a cancellative monoid and let G be an HNNextension of H with finite associated subgroups A,B ≤ H. We show that, if equations are algorithmically solvable in H, then they are also algorithmically solvable in G. The result also holds for equations with rational constraints and for ..."
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Cited by 3 (3 self)
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. Keywords: Equations; groups and monoids; HNNextensions; amalgamated product.
RELATIVE DEHN FUNCTIONS OF AMALGAMATED PRODUCTS AND HNN–EXTENSIONS.
, 2004
"... Abstract. We obtain an upper bound for relative Dehn functions of amalgamated products and HNN–extensions with respect to certain collections of subgroups. Our main results generalize the combination theorems for relatively hyperbolic groups proved by Dahmani. 1. ..."
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Cited by 5 (0 self)
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Abstract. We obtain an upper bound for relative Dehn functions of amalgamated products and HNN–extensions with respect to certain collections of subgroups. Our main results generalize the combination theorems for relatively hyperbolic groups proved by Dahmani. 1.
Positive theories of HNNextensions and amalgamated free products
, 2006
"... It is shown that the positive firstorder theory of an HNNextension G = 〈H, t; t −1 at = ϕ(a)(a ∈ A) 〉 can be reduced to the existential firstorder theory of G provided that A and B are proper subgroups of the base group H with A∩B finite. For an amalgamated free product G = H ∗A J, we show that th ..."
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Cited by 4 (4 self)
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It is shown that the positive firstorder theory of an HNNextension G = 〈H, t; t −1 at = ϕ(a)(a ∈ A) 〉 can be reduced to the existential firstorder theory of G provided that A and B are proper subgroups of the base group H with A∩B finite. For an amalgamated free product G = H ∗A J, we show
Compressed word problems in HNNextensions and amalgamated products
, 811
"... Abstract. It is shown that the compressed word problem for an HNNextension 〈H,t  t −1 at = ϕ(a)(a ∈ A) 〉 with A finite is polynomial time Turingreducible to the compressed word problem for the base group H. An analogous result for amalgamated free products is shown as well. 1 ..."
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Cited by 2 (1 self)
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Abstract. It is shown that the compressed word problem for an HNNextension 〈H,t  t −1 at = ϕ(a)(a ∈ A) 〉 with A finite is polynomial time Turingreducible to the compressed word problem for the base group H. An analogous result for amalgamated free products is shown as well. 1
SEMISTABILITY OF AMALGAMATED PRODUCTS, HNNEXTENSIONS, AND ALL ONERELATOR GROUPS
, 1992
"... Semistability at infinity is a geometric property used in the study of ends of finitely presented groups. If a finitely presented group G is semistable at infinity, then sophisticated invariants for G, such as the fundamental group at an end of G, can be defined (see [10]). It is unknown whether or ..."
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Cited by 4 (0 self)
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Semistability at infinity is a geometric property used in the study of ends of finitely presented groups. If a finitely presented group G is semistable at infinity, then sophisticated invariants for G, such as the fundamental group at an end of G, can be defined (see [10]). It is unknown whether or not all finitely presented groups
On the rational subset problem for groups
, 2007
"... We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN exten ..."
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Cited by 14 (10 self)
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We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN
AN HNNEXTENSION WITH CYCLIC ASSOCIATED SUBGROUPS AND WITH UNSOLVABLE CONJUGACY PROBLEM
"... Abstract. In this paper, we consider the conjugacy problem for HNNextensions of groups with solvable conjugacy problem for which the associated subgroups are cyclic. An example of such a group with unsolvable conjugacy problem is constructed. A similar construction is given for free products with am ..."
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Cited by 1 (0 self)
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Abstract. In this paper, we consider the conjugacy problem for HNNextensions of groups with solvable conjugacy problem for which the associated subgroups are cyclic. An example of such a group with unsolvable conjugacy problem is constructed. A similar construction is given for free products
A RELATIONSHIP BETWEEN HNN EXTENSIONS AND AMALGAMATED FREE PRODUCTS IN OPERATOR ALGEBRAS
, 2006
"... Abstract. With a minor change made in the previous construction in [19] we observe that any reduced HNN extension is precisely a compressed algebra of a certain reduced amalgamated free product in both the von Neumann algebra and the C ∗algebra settings. It is also pointed out that the same fact ho ..."
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Abstract. With a minor change made in the previous construction in [19] we observe that any reduced HNN extension is precisely a compressed algebra of a certain reduced amalgamated free product in both the von Neumann algebra and the C ∗algebra settings. It is also pointed out that the same fact
Results 1  10
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218