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.
Muhie, S., Russo, F. (2021). The probability of commuting subgroups in arbitrary lattices of subgroups. International Journal of Group Theory, 10(3), 125-135. doi: 10.22108/ijgt.2020.122081.1604
MLA
Seid Kassaw Muhie; Francesco G. Russo. "The probability of commuting subgroups in arbitrary lattices of subgroups". International Journal of Group Theory, 10, 3, 2021, 125-135. doi: 10.22108/ijgt.2020.122081.1604
HARVARD
Muhie, S., Russo, F. (2021). 'The probability of commuting subgroups in arbitrary lattices of subgroups', International Journal of Group Theory, 10(3), pp. 125-135. doi: 10.22108/ijgt.2020.122081.1604
VANCOUVER
Muhie, S., Russo, F. The probability of commuting subgroups in arbitrary lattices of subgroups. International Journal of Group Theory, 2021; 10(3): 125-135. doi: 10.22108/ijgt.2020.122081.1604
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