Abstract
We establish a new connection between local and large-scale structure in compactly generated totally disconnected locally compact (t.d.l.c.) groups G , finding a sufficient condition for G to have more than one end in terms of its compact subgroups. The condition actually results in an action of a quotient group G/N on a tree with faithful micro-supported action on the boundary, where N is compact, and is closely related to the Boolean algebra formed by the centralisers of the subgroups of G/N with open normaliser. As an application, we find a sufficient condition, given a one-ended t.d.l.c. group G , for all direct factors of open subgroups of G to be trivial or open.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
