Small cancellation theory and automatic groups

Gersten, S. M.; Short, Hamish

doi:10.1007/bf01233430

Cited by 130 publications

(154 citation statements)

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“…Since none of the presentations in [7,Main Theorem] and in [9, Theorem 8.1] are ðm; kÞ-special it follows that G always has a free subgroup of rank 2; in particular G is nonelementary. Statements (ii), (iv) and (v) now follow from [21] since in these cases G is hyperbolic by [11,Corollary 4.1]. Let m ¼ 2 and k ¼ 4.…”

Section: Definitionmentioning

confidence: 99%

On the SQ-universality of groups with special presentations

Edjvet¹,

Vdovina²

2010

Journal of Group Theory

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Section: Definitionmentioning

confidence: 99%

On the SQ-universality of groups with special presentations

Edjvet¹,

Vdovina²

2010

Journal of Group Theory

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“…Bumagin [Bum04] proved the same for the conjugacy problem. Virtually central extensions of hyperbolic groups are biautomatic [NR97], in particular, they have solvable word problem, and also solvable conjugacy problem [GS91a]. Finitely generated virtually nilpotent groups are polycyclicby-finite, and hence they are conjugacy separable [Rem69,For76], which implies that they have solvable conjugacy problem [Mos66].…”

Section: A-regular Metrics Of Negative Curvaturementioning

confidence: 99%

Complex hyperbolic hyperplane complements

Belegradek

2011

Math. Ann.

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Abstract. We study spaces obtained from a complete finite volume complex hyperbolic n -manifold M by removing a compact totally geodesic complex (n − 1) -submanifold S . The main result is that the fundamental group of M \ S is relatively hyperbolic, relative to fundamental groups of the ends of M \S , and M \S admits a complete finite volume A -regular Riemannian metric of negative sectional curvature.It follows that for n > 1 the fundamental group of M \ S satisfies Mostow-type Rigidity, has solvable word and conjugacy problems, has finite asymptotic dimension and rapid decay property, satisfies Borel and BaumConnes conjectures, is co-Hopf and residually hyperbolic, has no nontrivial subgroups with property (T), and has finite outer automorphism group. Furthermore, if M is compact, then the fundamental group of M \ S is biautomatic and satisfies Strong Tits Alternative.

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“…We use the following definitions from [GS1], [GS2]: Definition 7.1. An A 2 complex is a 2-dimensional CW-complex equipped with a metric with all 2-cells isometric to equilateral triangles.…”

Section: Curvature Of Doodle Groupsmentioning

confidence: 99%

“…Also, for some special types of doodles, we prove that their fundamental groups are automatic. The proof uses a theorem of Gersten and Short [GS1], [GS2] that the fundamental group of a 2-complex of non-positive curvature, modelled on equilateral triangles, is automatic.…”

Section: Introductionmentioning

confidence: 99%