Groups of permutation projective dimension two
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- by James E. Arnold PDF
- Proc. Amer. Math. Soc. 91 (1984), 505-509 Request permission
Abstract:
In previous papers we developed a version of homological algebra for $Z[G]$ modules ($G$ a finite group) using summands of permutation modules in place of projective modules. The resulting theory is more discriminating than the usual homological algebra. For example, an f.g. $Z$-torsion free $Z[G]$ module is either projective or has infinite projective dimension, whereas for $G$ cyclic, all f.g. $Z[G]$ modules have permutation projective dimension one. In this paper we apply results of Endo and Miyata on permutation projective modules to characterize groups of dimension two.References
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- Shizuo Endô and Takehiko Miyata, On a classification of the function fields of algebraic tori, Nagoya Math. J. 56 (1975), 85–104. MR 364203 —, Integral representations with trivial first cohomology groups, preprint.
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 505-509
- MSC: Primary 20J06; Secondary 18G20
- DOI: https://doi.org/10.1090/S0002-9939-1984-0746077-6
- MathSciNet review: 746077