Invariable generation of infinite groups

William M. Kantor, Alexander Lubotzky*, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

A subset S of a group G invariably generates G if G=〈sg(s)|s∈S〉 for each choice of g(s)∈G, s∈S. In this paper we study invariable generation of infinite groups, with emphasis on linear groups. Our main result shows that a finitely generated linear group is invariably generated by some finite set of elements if and only if it is virtually solvable. We also show that the profinite completion of an arithmetic group having the congruence subgroup property is invariably generated by a finite set of elements.

Original languageAmerican English
Pages (from-to)296-310
Number of pages15
JournalJournal of Algebra
Volume421
DOIs
StatePublished - 1 Jan 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

  • Congruence subgroup property
  • Invariable generation
  • Linear groups
  • Profinite groups

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