The transfer in modular invariant theory

We study the transfer homomorphism in modular invariant theory paying parti cular attention to the image of the transfer which is a proper non-zero ide al in the ring of invariants. We prove that, for a p-group over F-p whose r ing of invariants is a polynomial algebra, the image of the transfer is a p rincipal ideal. We compute the image of the transfer for SLn(F-q) and GL(n) (F-q) showing that both ideals are principal. We prove that, for a permutat ion group, the image of the transfer is a radical ideal and for a cyclic pe rmutation group the image of the transfer is a prime ideal. (C) 1999 Elsevi er Science B.V. All rights reserved.