Malnormal subgroups of free groups

Benjamin Fine, Alexei Myasnikov, Gerhard Rosenberger

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

A subgroup H of a group G is malnormal if for any g ∈ G, g ∈ H, then g-1Hg ∩ H = {1}. Here we give a complete characterization of rank 2 malnormal subgroups of free groups. In particular a 2-generator subgroup of a free group F is malnormal if and only if it is isolated and malnormal on generators. The result is not true for greater rank subgroups. This theorem was motivated by a recent algorithm developed by Baumslag, Myasnikov and Remeslennikov that decides whether a subgroup of a free group is malnormal or not.

Original languageEnglish
Pages (from-to)4155-4164
Number of pages10
JournalCommunications in Algebra
Volume30
Issue number9
DOIs
StatePublished - 1 Sep 2002

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