### 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 language | English |
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Pages (from-to) | 428-433 |

Number of pages | 6 |

Journal | Journal of Algebra |

Volume | 310 |

Issue number | 1 |

Early online date | 4 Jan 2007 |

DOIs | |

Publication status | Published - 1 Apr 2007 |

### Keywords

- generating hypothesis
- stable module category
- ghost map

## Cite this

Benson, D. J., Chebolu, S. K., Christensen, J. D., & Minác, J. (2007). The generating hypothesis for the stable module category of a p-group.

*Journal of Algebra*,*310*(1), 428-433. https://doi.org/10.1016/j.jalgebra.2006.12.013