University of IsfahanInternational Journal of Group Theory2251-765010320210901The probability of commuting subgroups in arbitrary lattices of subgroups1251352455110.22108/ijgt.2020.122081.1604ENSeid KassawMuhieDepartment of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X1, Rondebosch, 7701,
Cape Town, South AfricaFrancesco G.RussoDepartment of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X1, Rondebosch, 7701,
Cape Town, South Africa0000-0002-5889-783XJournal Article20200310A 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.https://ijgt.ui.ac.ir/article_24551_eb9d618b2894cd2f45f542b6ef64c301.pdf