### Abstract

Let G be a simple algebraic group of type G2 over an algebraically closed field of characteristic 2. We give an example of a finite group Γ with Sylow 2-subgroup Γ2 and an infinite family of pairwise non-conjugate homomorphisms ρ: Γ → G whose restrictions to Γ2 are all conjugate. This answers a question of Burkhard Külshammer from 1995. We also give an action of Γ on a connected unipotent group V such that the map of 1-cohomologies H1(Γ, V) → H1(Γp, V) induced by restriction of 1-cocycles has an infinite fibre.

To Burkhard Külshammer on his sixtieth birthday

To Burkhard Külshammer on his sixtieth birthday

Original language | English |
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Pages (from-to) | 463-470 |

Number of pages | 8 |

Journal | Israel Journal of Mathematics |

Volume | 214 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jul 2016 |

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### Cite this

Bate, M., Martin, B., & Rohrle, G. (2016). On a question of Külshammer for representations of finite groups in reductive groups.

*Israel Journal of Mathematics*,*214*(1), 463-470. https://doi.org/10.1007/s11856-016-1337-2