@article {
author = {Muhie, Seid Kassaw and Russo, Francesco G.},
title = {The probability of commuting subgroups in arbitrary lattices of subgroups},
journal = {International Journal of Group Theory},
volume = {10},
number = {3},
pages = {125-135},
year = {2021},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2020.122081.1604},
abstract = {A finite group $G$, in which two randomly chosen subgroups $H$ and $K$ commute, has been classified by Iwasawa in 1941. It is possible to define a probabilistic notion, which ``measures the distance'' of $G$ from the groups of Iwasawa. Here we introduce the generalized subgroup commutativity degree $gsd(G)$ for two arbitrary sublattices $\mathrm{S}(G)$ and $\mathrm{T}(G)$ of the lattice of subgroups $\mathrm{L}(G)$ of $G$. Upper and lower bounds for $gsd(G)$ are shown and we study the behaviour of $gsd(G)$ with respect to subgroups and quotients, showing new numerical restrictions.},
keywords = {Subgroup commutativity degree,Dihedral groups,Sublattices,Elementary abelian $p$-groups,polynomial functions},
url = {https://ijgt.ui.ac.ir/article_24551.html},
eprint = {https://ijgt.ui.ac.ir/article_24551_eb9d618b2894cd2f45f542b6ef64c301.pdf}
}