The so--called subgroup commutativity degree $sd(G)$ of a finite group $G$ is the number of permuting subgroups $(H,K) \in \mathrm{ L}(G) \times \mathrm{ L}(G)$, where $\mathrm{ L}(G)$ is the subgroup lattice of $G$, divided by $|\mathrm{ L}(G)|^2$. It allows us to measure how $G$ is far from the celebrated classification of quasihamiltonian groups of K. Iwasawa. Here we generalize $sd(G)$, looking at suitable sublattices of $\mathrm{ L}(G)$, and show some new lower bounds.
Categories: math.GR math.CO
