Stefan-Christoph Virchow

activity

20162019

collaborators

4 papers

math.GR2019

Random Generation of the Special Linear Group

Sean Eberhard, Stefan-C. Virchow

It is well known that the proportion of pairs of elements of $SL (n, q)$ which generate the group tends to $1$ as $q^{n} \to \infty$ . This was proved by Kantor and Lubotz…

math.GR2017

The Multiplicities of Root Number Functions

Stefan-Christoph Virchow

We consider the $q$ th root number function for the symmetric group. Our aim is to develop an asymptotic formula for the multiplicities of the $q$ th root number function as $q$ tend…

math.GR2017

Application of Character Estimates to the Number of $T_{2}$ -Systems of the Alternating Group

Stefan-Christoph Virchow

We use character theory and character estimates to show that the number of $T_{2}$ -systems of $A_{n}$ is at least \begin{equation*} \frac{1}{8n\sqrt{3}}\exp\left(\frac{2π}{\sqrt{6}}n^{…

math.GR2016

The Probability of Generating the Symmetric Group

Sean Eberhard, Stefan-Christoph Virchow

We consider the probability $p (S_{n})$ that a pair of random permutations generates either the alternating group $A_{n}$ or the symmetric group $S_{n}$ . Dixon (1969) proved that $p (S_{n})$ …

Random Generation of the Special Linear Group

The Multiplicities of Root Number Functions

Application of Character Estimates to the Number of T2​-Systems of the Alternating Group

The Probability of Generating the Symmetric Group

Application of Character Estimates to the Number of $T_{2}$ -Systems of the Alternating Group