Geodesic
Rings of Invariants and p-Sylow Subgroups
Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 42-47

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DOI

Let V be a vector space of dimension n over a field k of characteristic p. Let G ⊆ Gl(V) be a finite group with p-Sylow subgroup P. G and P act on the symmetric algebra R of V. Denote the respective rings of invariants by RG and Rp. We show that if Rp is Cohen-Macaulay (CM) so also is RG, generalizing a result of M. Hochster and J. A. Eagon. If P is normal in G and G is generated by P and pseudo-reflections, we show that if RG is CM so also is Rp. However, in general, RG may even be polynomial with Rp not CM. Finally, we give a procedure for determining a set of generators for RG given a set of generators for Rp.
DOI : 10.4153/CMB-1991-007-0
Mots-clés : Invariant theory, 13F20 
Campbell, H. E. A.; Hughes, I.; Pollack, R. D. Rings of Invariants and p-Sylow Subgroups. Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 42-47. doi: 10.4153/CMB-1991-007-0
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     title = {Rings of {Invariants} and {p-Sylow} {Subgroups}},
     journal = {Canadian mathematical bulletin},
     pages = {42--47},
     year = {1991},
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     number = {1},
     doi = {10.4153/CMB-1991-007-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-007-0/}
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