Abstract
We consider a block B of a finite group with defect group D≅(C2m)n and inertial quotient E containing a Singer cycle (an element of order 2n−1). This implies E=E⋊F, where E≅C2n−1, F≤Cn, and E acts transitively on the elements in D of order 2. We classify the basic Morita equivalence classes of B over a complete discrete valuation ring O: when m=1, B is basic Morita equivalent to the principal block of one of SL2(2n)⋊F, D⋊E, or J1 (where J1 occurs only when n=3). When m>1, B is basic Morita equivalent to D⋊E.
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.
