Pablo Spiga (University of Western Australia, Perth, Avstralija): How non-abelian is a non-abelian group?

Povzetek: There are many invariants associated to a group to establish how far from being abelian a given group is. In this talk we are interested in the maximal number $\omega(G)$ of pairwise non-commuting elements of $G$. This number was introduced by Paul Erdos and a first deep investigation was done by B. H. Neumann. In this talk we study $\omega(G)$ for $G$ the symmetric group and for $G$ the general linear group.