On the distribution of the density of maximal order elements in general linear groups

In this paper we consider the density of maximal order elements in $mathrm{GL}_n(q)$. Fixing any of the rank $n$ of the group, the characteristic $p$ or the degree $r$ of the extension of the underlying field $mathbb{F}_q$ of size $q=p^r$, we computethe expected value of the said density and establish that it follows a distribution law.

On the subgroup permutability degree of the simple Suzuki groups

We prove that the subgroup permutability degree of the simple Suzuki groups vanishes asymptotically. In the course of the proof we establish that the limit of the probability of a subgroup of $Sz(q)$ being a 2-group is equal to 1.