Abstract
In [4], B.H. Neumann asked whether it is true that every characteristic subgroup W of a free group F of infinite rank is fully invariant, and in [51 he conjectured that this is so. Cohen [1] provided support for the conjecture by proving that W is always fully invariant when F/W is abelian-by-nilpotent. However two examples will be described here of characteristic subgroups of the free group F of countable rank which are not fully invariant. Also, a proof will be given of the fact that there are continuously many characteristic subgroups of F which are not fully invariant.
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.
