A note on $G$-invariant forms
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- by Stephen M. Gagola PDF
- Proc. Amer. Math. Soc. 123 (1995), 3301-3304 Request permission
Abstract:
If G is a finite group, the reduction $\bmod \; p$ of a module supporting a nondegenerate G-invariant form need not itself support such a form. However, under a suitable hypothesis on the splitting field (quadratric closure) and a carefully chosen lattice within the module (for reduction $\bmod \; p$), this will always be the case. The argument given is elementary and self-contained.References
- Stephen M. Gagola Jr. and Sidney C. Garrison III, Real characters, double covers, and the multiplier. II, J. Algebra 98 (1986), no. 1, 38–75. MR 825134, DOI 10.1016/0021-8693(86)90014-1
- David M. Goldschmidt, Lectures on character theory, Publish or Perish, Inc., Wilmington, Del., 1980. MR 575526
- Daniel Quillen, The Adams conjecture, Topology 10 (1971), 67–80. MR 279804, DOI 10.1016/0040-9383(71)90018-8 J. G. Thompson, Bilinear forms in characteristic p and the Frobenius-Schur indicator, Group Theory (Beijing 1984), Lecture Notes in Math., vol. 1185, Springer-Verlag, Berlin and New York, 1985, pp. 221-230.
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3301-3304
- MSC: Primary 20C11; Secondary 20C05, 20C20
- DOI: https://doi.org/10.1090/S0002-9939-1995-1291768-1
- MathSciNet review: 1291768