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- W2126177866 abstract "Let the finite group G act linearly on the vector space V over the field k of arbitrary characteristic, and let H < G be a subgroup. The extension of invariant rings k[V]G ⊂ k[V]H is studied using modules of covariants. An example of our results is the following. Let W be the subgroup of G generated by the reflections in G. A classical theorem due to Serre says that if k[V] is a free k[V]G-module then G = W. We generalize this result as follows. If k[V]H is a free k[V]G-module, then G is generated by H and W. Furthermore, the invariant ring k[V]H ∩ W is free over k[V]W and is generated as an algebra by H-invariants and W-invariants." @default.
- W2126177866 created "2016-06-24" @default.
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- W2126177866 date "2009-12-13" @default.
- W2126177866 modified "2023-09-30" @default.
- W2126177866 title "Modules of covariants in modular invariant theory" @default.
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- W2126177866 doi "https://doi.org/10.1112/plms/pdp044" @default.
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