The nonrealizability of modular rings of polynomial invariants by the cohomology of a topological space
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- by Larry Smith PDF
- Proc. Amer. Math. Soc. 86 (1982), 339-340 Request permission
Abstract:
Let$G < {\text {GL}}(n;{{\mathbf {F}}_p})$ be a $p$-group, $p$ an odd prime, and ${R^*}: = {{\mathbf {F}}_p}{[{x_1}, \ldots ,{x_n}]^G}$ the ring of invariants. The purpose of this note is to prove that in the case where ${R^*}$ is a graded polynomial algebra, where $\deg {x_1} = \cdots = \deg {x_n} = 2$, then there is no space $X$ such that ${H^*}(X:{{\mathbf {F}}_p}) \simeq {R^*}$. This complements the work of Clark and Ewing [3] and Adams and Wilkerson [1] on the case $p\nmid [G;1]$.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 339-340
- MSC: Primary 55R35; Secondary 55S10
- DOI: https://doi.org/10.1090/S0002-9939-1982-0667302-4
- MathSciNet review: 667302