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.
The probability of commuting subgroups in arbitrary lattices of subgroups
Russo F
Primo
2021-01-01
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
