## Abstract

Let F and K be algebraically closed fields of characteristics p > 0 and 0, respectively. For any finite group G we denote by K R_{F} (G) = K ⊗_{Z} G_{0} (F G) the modular representation algebra of G over K where G_{0} (F G) is the Grothendieck group of finitely generated F G-modules with respect to exact sequences. The usual operations induction, inflation, restriction, and transport of structure with a group isomorphism between the finitely generated modules of group algebras over F induce maps between modular representation algebras making K R_{F} an inflation functor. We show that the composition factors of K R_{F} are precisely the simple inflation functors S_{C, V}^{i} where C ranges over all nonisomorphic cyclic p^{′}-groups and V ranges over all nonisomorphic simple K Out (C)-modules. Moreover each composition factor has multiplicity 1. We also give a filtration of K R_{F}.

Original language | English |
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Pages (from-to) | 140-179 |

Number of pages | 40 |

Journal | Journal of Algebra |

Volume | 318 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Dec 2007 |

Externally published | Yes |

## Keywords

- (Global) Mackey functor
- Biset functor
- Composition factors
- Filtration
- Inflation functor
- Modular representation algebra
- Multiplicity