The Hanna Neumann conjecture for Demushkin Groups

Abstract

We confirm the Hanna Neumann conjecture for topologically finitely generated closed subgroups $U$ and $W$ of a nonsolvable Demushkin group $G$. Namely, we show that \begin{equation*} \sum_{g \in U \backslash G/W} \bar d(U \cap gWg^{-1}) \leq \bar d(U) \bar d(W) \end{equation*} where $\bar{d}(K)=\max \{d(K)-1,0\}$ and $d(K)$ is the least cardinality of a topological generating set for the group $K$.