Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-07T23:02:22.036Z Has data issue: false hasContentIssue false

STRONGLY BOUNDED LOCALLY INDICABLE GROUPS

Published online by Cambridge University Press:  19 February 2021

SAMUEL M. CORSON*
Affiliation:
School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol, BS8 1UG, UK

Abstract

We give the construction of some locally indicable groups which are strongly bounded (every abstract action on a metric space has bounded orbits).

Type
Research Article
Copyright
© 2021 Australian Mathematical Publishing Association Inc.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This work was supported by the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-20150554) and the Heilbronn Institute for Mathematical Research Bristol, UK.

References

Bergman, G., ‘Right-orderable groups that are not locally indicable’, Pacific J. Math. 147 (1991), 243248.10.2140/pjm.1991.147.243CrossRefGoogle Scholar
Bergman, G., ‘Generating infinite symmetric groups’, Bull. Lond. Math. Soc. 38 (2006), 429440.CrossRefGoogle Scholar
de Cornulier, Y., ‘Strongly bounded groups and infinite powers of finite groups’, Comm. Algebra 34 (2006), 23372345.10.1080/00927870600550194CrossRefGoogle Scholar
Droste, M. and Holland, W. C., ‘Generating automorphism groups of chains’, Forum Math. 17 (2005), 699710.10.1515/form.2005.17.4.699CrossRefGoogle Scholar
Karrass, A. and Solitar, D., ‘Subgroups of HNN groups and groups with one defining relation’, Canad. J. Math. 23 (1971), 627643.10.4153/CJM-1971-070-xCrossRefGoogle Scholar
Navas, A., ‘On the dynamics of (left) orderable groups’, Ann. Inst. Fourier 60 (2010), 16851740.CrossRefGoogle Scholar