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The Reduction of an RG–Lattice Modulo pn

Published online by Cambridge University Press:  20 November 2018

Peter Symonds
Peter Symonds*
Affiliation:
McMaster University, Hamilton, Ontario
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We define the cover of an RG-module V to consist of an RG lattice Ṽ and a homomorphism π : Ṽ→ V such that π induces an isomorphism on Ext*RG(M, —) for any RG-lattice M. Here G is a finite group and, for simplicity in this introduction, R is a complete discrete valuation ring of characteristic zero with prime element p and perfect valuation class field. Let pn(G) be the highest power of p that divides |G| and, given an RG-lattice M, let pn(M) be the smallest power of p such that pn(M) idM : M→M factors through a projective lattice: n(M)≦n(G).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 2 , 01 April 1990 , pp. 342 - 364
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Benson, D.J. and Carlson, J.F., Nilpotent elements in the Green ring, J. Algebra 104 (1986), 329–350.Google Scholar
2. Curtis, C.W. and Reiner, I., Methods of representation theory, vol. 1 (Wiley, New York, 1981).Google Scholar
3. Gruenberg, K.W., Partial Euler characteristics of finite groups and the decomposition of lattices, Proc. London Math. Soc. 48 (1984), 91–107.Google Scholar
4. Jones, A. and Michler, G.O., On the structure of the integral Green ring of a cyclic group of order p2 , in Representation theory II, groups and orders, Lecture Notes in Math. 1178 (Springer Verlag, Berlin/Heidelberg, 1984).Google Scholar
5. Maranda, J.M., On p-adic integral representations of finite groups, Can. J. Math. 45 (1953), 344–355.Google Scholar
6. Symonds, P.A., Cohomological methods in integral representation theory, J. Pure and Applied Algebra 56 (1989), 163–176.Google Scholar