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

Alan D. Logan

Research output: Contribution to journalArticle

Abstract

Fix an equilateral triangle group Ti=〈a,b;ai,bi,(ab)i〉 with i≥6 arbitrary. Our main result is: for every presentation P of every countable group Q there exists an HNN-extension TP of Ti such that Out(TP)≅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.

LanguageEnglish
Pages116-152
Number of pages37
JournalAdvances in Mathematics
Volume353
Early online date2 Jul 2019
DOIs
Publication statusPublished - 7 Sep 2019

Fingerprint

Triangle Group
HNN Extension
Outer Automorphism Groups
Subgroup
Equilateral triangle
Cancellation
Categorical
Countable
Arbitrary

Keywords

  • Automorphisms of free groups
  • HNN-extensions
  • Outer automorphism groups
  • Small cancellation theory
  • Triangle groups

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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Every group is the outer automorphism group of an HNN-extension of a fixed triangle group. / Logan, Alan D.

In: Advances in Mathematics, Vol. 353, 07.09.2019, p. 116-152.

Research output: Contribution to journalArticle

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