Abstract
Let G be a p-group, a its element of prime order p, and CG(a) a Cernikov group. We prove that either G is a Cernikov group, or G possesses a non-locally finite section w.r.t. a Cernikov subgroup in which a maximal locally finite subgroup containing an image of a is unique. Moreover, it is shown that the set of groups which satisfy the first part of the alternative is countable, while the set of groups which comply with the second is of the power of the continuum for every odd p.
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.
