Rings of Invariants and p-Sylow Subgroups
1991 ◽
Vol 34
(1)
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pp. 42-47
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Keyword(s):
AbstractLet 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.
2021 ◽
Vol 58
(2)
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pp. 147-156
Keyword(s):
2008 ◽
Vol 01
(03)
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pp. 369-382
Keyword(s):
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2014 ◽
Vol 90
(2)
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pp. 220-226
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Keyword(s):
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2019 ◽
Vol 12
(2)
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pp. 571-576
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1968 ◽
Vol 20
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pp. 1256-1260
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