Simultaneous Conjugacy Classes of Finite $p$-groups of rank $\le 5$

Abstract

For a finite group $G$, we consider the problem of counting simultaneous conjugacy classes of $n$-tuples and simultaneous conjugacy classes of commuting $n$-tuples in $G$. Let ${\alpha }_{G,n}$ denote the number of simultaneous conjugacy classes of $n$-tuples, and ${\beta }_{G,n}$ the number of simultaneous conjugacy classes of commuting $n$-tuples in $G$. The generating functions $A_G(t)={\sum }_{n\ge 0}{\alpha }_{G,n}{t}^n,$ and $B_G(t)={\sum }_{n\ge 0}{\beta }_{G,n}{t}^n$ are rational functions of $t$. This paper concern studied of normalized functions $A_G(t/|G|)$ and $B_G(t/|G|)$ for finite $p$-groups of rank at most $5$.

arXiv admin note: substantial text overlap with arXiv:1905.07957

References in corpus (3)

• Simultaneous Similarity Classes of Commuting matrices over a finite field
• Asymptotic of Number of Similarity Classes of Commuting Tuples
• Simultaneous Conjugacy Classes of Finite $p$-groups of rank $\le 5$

Cited by in corpus (2)

• Simultaneous Conjugacy Classes of Finite $p$-groups of rank $\le 5$
• Asymptotics of commuting probabilities in reductive algebraic groups