Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-19T06:33:17.946Z Has data issue: false hasContentIssue false

Carlson varieties and Chouinard's theorem

Published online by Cambridge University Press:  04 October 2011

Robert C. Andrews
Affiliation:
Merton College, Oxford

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
Copyright
Copyright © Cambridge Philosophical Society 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Alperin, J. and Evens, L.. Representations, resolutions, and Quillen's dimension theorem. J. Pure Appl. Algebra 22 (1981), 19.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), 4955.CrossRefGoogle Scholar
[5] Carlson, J. F.. Periodic modules with large periods. Proc. Amer. Math. Soc. 76 (1979), 209215.CrossRefGoogle Scholar
[6] Carlson, J. F.. The varieties and the cohomology ring of a module. J. Algebra 85 (1983), 104143.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), 278302.CrossRefGoogle Scholar
[9] Dade, E. C.. Endo-permutation modules over p-groups II. Ann. of Math. (2) 108 (1978). 317346.CrossRefGoogle Scholar
[10] Evens, L.. The cohomology ring of a finite group. Trans. Amer. Math. Soc. 101 (1961), 224239.CrossRefGoogle Scholar
[11] Serre, J.-P.. Sur la dimension cohomologique des groupes profinis. Topology 3 (1965), 413420.CrossRefGoogle Scholar