## Abstract

Let k be an algebraically closed field of characteristic p, and let O be either k or its ring of Witt vectors W(k). Let G be a finite group and B a block of OG with normal abelian defect group and abelian p′ inertial quotient L. We show that B is isomorphic to its second Frobenius twist. This is motivated by the fact that bounding Frobenius numbers is one of the key steps towards Donovan’s conjecture. For O=k, we give an explicit description of the basic algebra of B as a quiver with relations. It is a quantized version of the group algebra of the semidirect product P⋊L.

Original language | English |
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Pages (from-to) | 1437-1448 |

Number of pages | 12 |

Journal | Q. J. Math. |

Volume | 70 |

Issue number | 4 |

DOIs | |

Publication status | Published - 21 Oct 2019 |

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