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The probability of commuting subgroups in arbitrary lattices of subgroups | ||
| International Journal of Group Theory | ||
| مقاله 3، دوره 10، شماره 3، آذر 2021، صفحه 125-135 اصل مقاله (212.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2020.122081.1604 | ||
| نویسندگان | ||
| Seid Kassaw Muhie؛ Francesco G. Russo* | ||
| Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X1, Rondebosch, 7701, Cape Town, South Africa | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Subgroup commutativity degree؛ Dihedral groups؛ Sublattices؛ Elementary abelian $p$-groups؛ polynomial functions | ||
| مراجع | ||
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