Invariable generation and wreath products

Research output: Working paperWorking paper and Preprints

Abstract

Invariable generation is a topic that, until relatively recently, has predominantly been studied for finite groups. In 2014, Kantor, Lubotzky, and Shalev produced extensive tools for investigating invariable generation for infinite groups. Since their paper, various authors have investigated the property for particular infinite groups or families of infinite groups.

A group is invariably generated by a subset S if replacing each element of S with any of its conjugates still results in a generating set for G. In this paper we investigate how this property behaves with respect to wreath products. Our main work is to deal with the case where the base of $G\wr_XH$ is not invariably generated. We see both positive and negative results here depending on H and its action on X.
Original languageEnglish
Place of PublicationJournal of Group Theory
Pages79-93
Number of pages15
Volume24
DOIs
Publication statusPublished - 1 Jan 2021

Publication series

NameJournal of Group Theory
PublisherWalter de Gruyter GmbH
ISSN (Print)1433-5883

Bibliographical note

Publisher Copyright:
© 2020 Cox, published by De Gruyter 2021.

Keywords

  • Invariable generation
  • Infinite groups
  • Wreath products

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