## Abstract

Let G be a finite group with a subgroup H. Given a field k of characteristic p dividing the order of G, denote by mod kG the category of finite-dimensional over k left G-modules, and let be the full subcategory of mod kG determined by the relatively projective modules. Let 0⟶L⟶M⟶N⟶0 be an exact sequence in mod kG with L, M, N ∈. It is proved that the sequence is an almost split sequence in if and only if it is an almost split sequence in mod kG. This implies, together with a recent result of Carlson and Happel, that has almost split sequences if and only if it is closed under extensions, i.e., if and only if p is coprime to either the order of H or the index of H in G.

Original language | English (US) |
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Pages (from-to) | 943-947 |

Number of pages | 5 |

Journal | Proceedings of the American Mathematical Society |

Volume | 116 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1992 |

## Keywords

- Almost split sequence
- Finite group
- Relatively projective module

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics