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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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[1] S. Eberhard, Commuting probabilities of finite groups, Bull. London Math. Soc., 47 (2015) 769–808.
[2] P. Erd˝os and P. Tur´an, On some problems of a statistical group theory I, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 4 (1965) 175–186. [3] A. Erfanian, P. Lescot and R. Rezaei, On the relative commutativity degree of a subgroup of a finite group, Comm. Algebra, 35 (2007) 4183–4197. [4] S. Garion and A. Shalev, Commutator maps, measure preservation, and T-systems, Trans. Amer. Math. Soc., 361 (2009) 4631–4651. [5] W. Herfort, K. H. Hofmann and F. G. Russo, Periodic Locally Compact Groups, de Gruyter, Berlin, 2018.
[6] K. H. Hofmann and F. G. Russo, The probability that x and y commute in a compact group, Math. Proc. Camb. Philos. Soc., 153 (2012) 557–571. [7] K. Iwasawa, Uber die endlichen Gruppen und die Verb¨ande ihrer Untergruppen, ¨ J. Fac. Sci. Imp. Univ. Tokyo, Sect. I, 4 (1941) 171–199. [8] E. Kazeem, Subgroup commutativity degree of profinite groups, Topology Appl., 263 (2019) 1–15.
[9] M. S. Lazorec, Probabilistic aspects of ZM-groups, Comm. Algebra, 47 (2018) 541–552.
[10] M. S. Lazorec, Relative cyclic subgroup commutativity degrees of finite groups, Filomat, 33 (2019) 4021–4032.
[11] D. E. Otera and F. G. Russo, Subgroup S-commutativity degrees of finite groups, Bull. Belg. Math. Soc. Simon Stevin, 19 (2012) 373–382. [12] F. G. Russo, Strong subgroup commutativity degree and some recent problems on the commuting probabilities of elements and subgroups, Quaest. Math., 39 (2016) 1019–1036. [13] R. Schmidt, Subgroup Lattices of Groups, de Gruyter, Berlin, 1994.
[14] A. Shalev, Some Results and Problems in the Theory of Word Maps, Erd˝os Centennial, L. Lov´asz , I. Z. Ruzsa, V. T. S´os and (eds), Bolyai Society Mathematical Studies, 25, Springer, Berlin, 2013 611–649. [15] M. Tˇarnˇauceanu, Subgroup commutativity degrees of finite groups, J. Algebra, 321 (2009) 2508–2520.
[16] M. Tˇarnˇauceanu, Addendum to: Subgroup commutativity degrees of finite groups, J. Algebra, 337 (2011) 363–368.
[17] M. Tˇarnˇauceanu, An arithmetic method of counting the subgroups of a finite abelian group, Bull. Math. Soc. Sci. Math. Roumanie, 53 (2010) 373–386. | ||
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