The Bass–Jiang group for automorphism-induced HNN-extensions

Logan, Alan D.

doi:10.1016/j.jalgebra.2018.10.014

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2019

Publication Types

Select...

Article3

Relationship

Self Cite3

Independent0

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Both corollaries relate to the subgroup-quotient N H (K)/K. This subgroup-quotient plays a central role in a framework for the construction of groups possessing certain properties and with specified outer automorphism group [Log15] (see also [Log16] [Log17]).…”

Section: Introductionmentioning

confidence: 99%

The residual finiteness of (hyperbolic) automorphism-induced HNN-extensions

Logan

2018

Communications in Algebra

Self Cite

View full text Add to dashboard Cite

We classify finitely generated, residually finite automorphisminduced HNN-extensions in terms of the residual separability of a single associated subgroup. This classification provides a method to construct automorphism-induced HNN-extensions which are not residually finite. We prove that this method can never yield a "new" counter-example to Gromov's conjecture on the residual finiteness of hyperbolic groups.

show abstract

Section: Introductionmentioning

confidence: 99%

The residual finiteness of (hyperbolic) automorphism-induced HNN-extensions

Logan

2018

Communications in Algebra

Self Cite

View full text Add to dashboard Cite

show abstract

Every group is the outer automorphism group of an HNN-extension of a fixed triangle group

Logan

2019

Advances in Mathematics

Self Cite

View full text Add to dashboard Cite

Fix an equilateral triangle group T i = a, b; a i , b i , (ab) i with i ≥ 6 arbitrary. Our main result is: for every presentation P of every countable group Q there exists an HNN-extension T P of T i such that Out(T P ) ∼ = Q. We construct the HNN-extensions explicitly, and examples are given. The class of groups constructed have nice categorical and residual properties. In order to prove our main result we give a method for recognising malnormal subgroups of small cancellation groups, and we introduce the concept of "malcharacteristic" subgroups.

show abstract