## Abstract

Let R be a local (commutative) ring and let p be a prime not invertible in R. Let G be a finite group of order divisible by p. It is well known that the group ring RG admits nonprojective lattices (e.g., R itself with the trivial action). For any element α∈H^{2}(G,R*) one can form the twisted group ring R^{α}G. The "twisting problem" asks whether there exists a class α s.t. the corresponding twisted group ring admits only projective lattices. For fields of characteristic p, the answer is in E. Aljadeff and D. J. S. Robinson [J. Pure Appl. Algebra94 (1994), 1-15]. Here we answer this question for rings of the form Z_{p}^{s}, s≥2. The main tools are the classification of modular representation of the Klein 4 group over Z_{2} and a Chouinard-like theorem [E. Aljadeff and Y. Ginosar, J. Algebra179 (1996), 599-606] for twisted group rings.

Original language | English |
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Pages (from-to) | 249-274 |

Number of pages | 26 |

Journal | Journal of Algebra |

Volume | 217 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jul 1999 |

Externally published | Yes |