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On The Top Degree of Coinvariants
International mathematics research notices
For a finite group G acting faithfully on a finite dimensional F-vector space V, we show that in the modular case, the top degree of the vector coinvariants grows unboundedly: _m→∞ F[V^m]_G=∞. In contrast, in the non-modular case we identify a situation where the top degree of the vector coinvariants remains constant. Furthermore, we present a more elementary proof of Steinberg's theorem which says that the group order is a lower bound for the dimension of the coinvariants which is sharp if and only if the invariant ring is polynomial.doi:10.1093/imrn/rnt158 fatcat:hyvq6w7yjrcn5iz75jlhpcggzu