Abstract
'. For finite nilpotent groups G and G', and a G-adapted ring S (the rational integers, for example), it is shown that any isomorphism between the centers of the group rings SG and SG' is monomial, i.e., maps class sums in SG to class sums in SG' up to multiplication with roots of unity. As a consequence, G and G' have identical character tables if and only if the centers of their integral group rings ZG and ZG' are isomorphic. In the course of the proof, a new proof of the class sum correspondence is given.
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.
