# Details of talk

Title | Minimal Permutation Representations of Groups |
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Presenter | Michael Hendriksen (University of Western Sydney) |

Author(s) | Mr Michael Hendriksen |

Session | n/a |

Time | |

Abstract | The minimal degree of a group $G$, denoted $\mu(G)$, is the smallest non-negative integer $n$ such that $G$ can be embedded into the symmetric group on $n$ elements. The minimal degree interacts in an interesting way with direct products and an effort has been made to classify groups $G$ and $H$ for which $\mu(G \times H) = \mu(G) + \mu(H)$, which is the largest possible minimal degree for a direct product in this manner. We shall give a short overview on the progress towards this goal, before looking at the progress towards, in a sense, the opposite goal - if $G$ and $H$ are two groups such that $\mu(G) \ge \mu(H)$, when does $\mu(G \times H) = \mu(G)$? |