Thirty-Third Annual Victorian Algebra Conference, Sydney, Australia, 2015

Register for: VAC33

Details of talk

TitleMinimal Permutation Representations of Groups
PresenterMichael 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 $\mu(G \times H) = \mu(G)$?