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 journalArticle

13 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

Cite this

The generating hypothesis for the stable module category of a p-group. / Benson, David John; Chebolu, Sunil K.; Christensen, J. Daniel; Minác, Ján.

In: Journal of Algebra, Vol. 310, No. 1, 01.04.2007, p. 428-433.

Research output: Contribution to journalArticle

Benson, David John ; Chebolu, Sunil K. ; Christensen, J. Daniel ; Minác, Ján. / The generating hypothesis for the stable module category of a p-group. In: Journal of Algebra. 2007 ; Vol. 310, No. 1. pp. 428-433.
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