Abstract
Let C p denote the cyclic group of order p where p ⩾ 3 is prime. We denote by V 3 the indecomposable three-dimensional representation of C p over a field F of characteristic p. We compute a set of generators, in fact a SAGBI basis, for the ring of invariants F [ V 3 ⊕ V 3 ] C p . Our main result confirms the conjecture of Shank [R.J. Shank, Classical covariants and modular invariants, in: H.E.A. Campbell, D.L. Wehlau (Eds.), Invariant Theory in All Characteristics, CRM Proc. Lecture Notes, vol. 35, Amer. Math. Soc., 2004, pp. 241–249], for this example, that all modular rings of invariants of C p are generated by rational invariants, norms and transfers.
Sign-in/Register to access full text options 
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.
