# Pure Maths Colloquium: Scott Harper

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

Where: | Physics Theatre C |

When: | Oct 13 2022 @ 16.00 |

Video: | Not recorded |

Speaker: | Scott Harper University of St Andrews |

Title: | Derangements, invariable generation and simple groups |

By a classical theorem of Jordan, every nontrivial finite group acting transitively on a set contains a derangement (an element with no fixed points). Much more is now known, especially in the context of (almost) simple groups. In this talk, I’ll discuss some strong versions of this result and some applications. I’ll then focus on the question of whether there exist almost simple groups with elements that are derangements in every faithful primitive action, and I’ll show how this solves a question of Garzoni about invariable generating sets for simple groups.