Details of talk
|Title||Minimal Permutation Representations of Groups|
|Presenter||Michael Hendriksen (University of Western Sydney)|
|Author(s)||Mr Michael Hendriksen|
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 $\mu(G \times H) = \mu(G)$?