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Freyd's generating hypothesis for groups with periodic cohomology

Authors
  • Chebolu, Sunil K.
  • Christensen, J. Daniel
  • Mináč, Ján
Type
Published Article
Publication Date
Mar 28, 2011
Submission Date
Oct 17, 2007
Identifiers
DOI: 10.4153/CMB-2011-090-5
Source
arXiv
License
Yellow
External links

Abstract

Let $G$ be a finite group and let $k$ be a field whose characteristic $p$ divides the order of $G$. Freyd's generating hypothesis for the stable module category of $G$ is the statement that a map between finite-dimensional $kG$-modules in the thick subcategory generated by $k$ factors through a projective if the induced map on Tate cohomology is trivial. We show that if $G$ has periodic cohomology then the generating hypothesis holds if and only if the Sylow $p$-subgroup of $G$ is $C_2$ or $C_3$. We also give some other conditions that are equivalent to the GH for groups with periodic cohomology.

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