Group extensions and tame pairs

Mihalik, Michael L.

doi:10.1090/s0002-9947-99-02015-2

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“…His approach resulted in various group-theoretical results which implied some special cases of the tame ends conjecture, (cf. [10], [11]). The author introduced in [ Let H be a subgroup of a group G. Choose the presentation G = X|R .…”

Section: Introductionmentioning

confidence: 99%

On tame subgroups of finitely presented groups

Gitik

2018

Ann. Math. Québec

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Section: Introductionmentioning

confidence: 99%

On tame subgroups of finitely presented groups

Gitik

2018

Ann. Math. Québec

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Tameness and geodesic cores of subgroups

Gitik¹

2000

J Aust Math Soc A

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Let N be a finitely generated normal subgroup of a finitely generated group G. We show that if the trivial subgroup is tame in the factor group G/N, then N is tame in G. We also give a short new proof of the fact that quasiconvex subgroups of negatively curved groups are tame. The proof utilizes the concept of the geodesic core of the subgroup and is related to the Dehn algorithm.2000 Mathematics subject classification: primary 57M07, 57M30,57N10, 20F32, 20F34.

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Measuring the tameness of almost convex groups

Hermiller¹,

Meier²

2000

Trans. Amer. Math. Soc.

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Abstract. A 1-combing for a finitely presented group consists of a continuous family of paths based at the identity and ending at points x in the 1-skeleton of the Cayley 2-complex associated to the presentation. We define two functions (radial and ball tameness functions) that measure how efficiently a 1-combing moves away from the identity. These functions are geometric in the sense that they are quasi-isometry invariants. We show that a group is almost convex if and only if the radial tameness function is bounded by the identity function; hence almost convex groups, as well as certain generalizations of almost convex groups, are contained in the quasi-isometry class of groups admitting linear radial tameness functions.

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Group extensions and tame pairs

Cited by 3 publications

References 13 publications

On tame subgroups of finitely presented groups

On tame subgroups of finitely presented groups

Tameness and geodesic cores of subgroups

Measuring the tameness of almost convex groups

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