The transfer in modular invariant theory

AbstractWe study the transfer homomorphism in modular invariant theory paying particular attention to the image of the transfer which is a proper non-zero ideal in the ring of invariants. We prove that, for a p-group over Fp whose ring of invariants is a polynomial algebra, the image of the transfer is a principal ideal. We compute the image of the transfer for SLn(Fq) and GLn(Fq) showing that both ideals are principal. We prove that, for a permutation group, the image of the transfer is a radical ideal and for a cyclic permutation group the image of the transfer is a prime ideal