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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Groups of permutation projective dimension two


Author: James E. Arnold
Journal: Proc. Amer. Math. Soc. 91 (1984), 505-509
MSC: Primary 20J06; Secondary 18G20
MathSciNet review: 746077
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0746077-6
PII: S 0002-9939(1984)0746077-6
Article copyright: © Copyright 1984 American Mathematical Society