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Carlson varieties and Chouinard's theorem

Published online by Cambridge University Press:  04 October 2011

Robert C. Andrews
Robert C. Andrews
Affiliation:
Merton College, Oxford
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Extract

Chouinard, in [8], proved the following remarkable result.

Theorem. Let k be a field of characteristic p and G be any finite group. Then a (finitely generated left) kG-module is protective if and only if it is free on restriction to all the elementary abelian p-subgroups of G.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 3 , May 1989 , pp. 423 - 439
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

[1] Alperin, J. and Evens, L.. Representations, resolutions, and Quillen's dimension theorem. J. Pure Appl. Algebra 22 (1981), 1–9.Google Scholar
[2] Andrews, R. C.. Modules over group algebras which are free on restriction to a maximal subgroup. Ph.D. Thesis, Univ. of Warwick (1987).Google Scholar
[3] Benson, D. J.. Modular Representation Theory: New Trends and Methods. Lecture Notes in Math vol. 1081 (Springer-Verlag, 1984).Google Scholar
[4] Carlson, J. F.. Free modules over some modular rings. J. Austral. Math. Soc. 21 (1976), 49–55.CrossRefGoogle Scholar
[5] Carlson, J. F.. Periodic modules with large periods. Proc. Amer. Math. Soc. 76 (1979), 209–215.CrossRefGoogle Scholar
[6] Carlson, J. F.. The varieties and the cohomology ring of a module. J. Algebra 85 (1983), 104–143.CrossRefGoogle Scholar
[7] Cartan, H. and Eilenberg, S.. Homological Algebra (Princeton University Press, 1956).Google Scholar
[8] Chouinard, L.. Projectivity and relative projectivity over group rings. J. Pure Appl. Algebra 7 (1976), 278–302.CrossRefGoogle Scholar
[9] Dade, E. C.. Endo-permutation modules over p-groups II. Ann. of Math. (2) 108 (1978). 317–346.CrossRefGoogle Scholar
[10] Evens, L.. The cohomology ring of a finite group. Trans. Amer. Math. Soc. 101 (1961), 224–239.CrossRefGoogle Scholar
[11] Serre, J.-P.. Sur la dimension cohomologique des groupes profinis. Topology 3 (1965), 413–420.CrossRefGoogle Scholar