Subgroup S-commutativity degrees of finite groups

Abstract

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.

8 pages; to appear in Bull. Belgian Math. Soc. with revisions

References in corpus (1)

• Relative n-isoclinism classes and relative n-th nilpotency degree of finite groups