The generating hypothesis for the stable module category of a p-group

David John Benson, Sunil K. Chebolu, J. Daniel Christensen, Ján Minác

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

Freyd's generating hypothesis, interpreted in the stable module category of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the induced map on Tate cohomology is trivial. We show that Freyd's generating hypothesis holds for a non-trivial finite p-group G if and only if G is either C-2 or C-3. We also give various conditions which are equivalent to the generating hypothesis.

Original languageEnglish
Pages (from-to)428-433
Number of pages6
JournalJournal of Algebra
Volume310
Issue number1
Early online date4 Jan 2007
DOIs
Publication statusPublished - 1 Apr 2007

Keywords

  • generating hypothesis
  • stable module category
  • ghost map

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