J. de la Nuez González

Average Numbers of Homomorphisms to Random Modules over Free Group Algebras

Let $F$ be a finitely generated free group, and let $L$ be a finitely presented $\mathbb{F}_q[F]$-module. We study the average number $\Lambda_L(n)$ of $\mathbb{F}_q[F]$-module homomorphisms from $L$ to an $\mathbb{F}_q[F]$-module of dimension $n$ over $\mathbb{F}_q$. We show that, for all sufficiently large $n$, the q...