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The Class Equation and the Commutativity Degree for Complete Hypergroups
Mathematics, 2020 The aim of this paper is to extend, from group theory to hypergroup theory, the class equation and the concept of commutativity degree. Both of them are studied in depth for complete hypergroups because we want to stress the similarities and the ...
Andromeda Cristina Sonea, Irina Cristea
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Correspondence between the Energy Equipartition Theorem in Classical Mechanics and Its Phase-Space Formulation in Quantum Mechanics [PDF]
Entropy, 2023 In classical physics, there is a well-known theorem in which it is established that the energy per degree of freedom is the same. However, in quantum mechanics, due to the non-commutativity of some pairs of observables and the possibility of having non ...
Esteban Marulanda +2 more
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On generalized commutativity degree of a finite group
Rocky Mountain Journal of Mathematics, 2011 Let \(G\) be a finite group. The generalized commutator of an \(n\)-tuple \((x_1,x_2,\dots,x_n)\in G^n\) is defined as the product \(x_1x_2\cdots x_nx_1^{-1}x_2^{-1}\cdots x_n^{-1}\). The object of this paper is to study the probability that the generalized commutator of an arbitrarily chosen \(n\)-tuple of group elements equals a given group element \(
Nath, R.K., Das, A.K.
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Subgroup commutativity degrees of finite groups
Journal of Algebra, 2009 Let \(G\) be a finite group and let \(L(G)\) be the set of subgroups of \(G\). The author defines the subgroup commutativity degree of \(G\) by \(\text{sd}(G)=|L(G)|^{-2}|\{(H,K)\in L(G)^2\mid HK=KH\}|\). Clearly, \(\text{sd}(G)\) is the probability that two subgroups of \(G\) permute. The author states some simple general properties of \(\text{sd}(G)\)
Marius T˘Arn˘Auceanu
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Finite Groups with Five Relative Commutativity Degrees
Results in Mathematics, 2022 We classify all finite groups with five relative commutativity degrees. Also, we give a partial answer to our previous conjecture on a lower bound of the number of relative commutativity degrees of finite groups.
Mohammad Farrokhi Derakhshandeh Ghouchan
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On the commutativity degree in finite Moufang loops [PDF]
International Journal of Group Theory, 2016 The textit{commutativity degree}, $Pr(G)$, of a finite group $G$ (i.e. the probability that two (randomly chosen) elements of $G$ commute with respect to its operation)) has been studied well by many authors.
Karim Ahmadidelir
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Energetic formulation of the subgroup commutativity degree
Nonlinear AnalysisFinite groups in which every pair of subgroups (H, K) satisfies H K = K H have been classified by Iwasawa, but only in the last decade it was introduced the notion of subgroup commutativity degree sd(G) of groups G. From restrictions of numerical nature
Seid Kassaw Muhie +2 more
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Commutativity Degree of Certain Finite AC-Groups [PDF]
Mathematics Interdisciplinary Research, 2021 For a finite group G, the probability of two elements of G that commute is the commutativity degree of G denoted by P(G). As a matter of fact, if C = {(a; b) ∈ G×G | ab = ba}, then P(G) = |C|/|G|2 .
Azizollah Azad, Sakineh Rahbariyan
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The probability of commuting subgroups in arbitrary lattices of subgroups [PDF]
International Journal of Group Theory, 2021 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.
Seid Kassaw Muhie, Francesco G. Russo
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Commutativity Degree of Crossed Modules
TURKISH JOURNAL OF MATHEMATICS, 2021 Summary: In this work, we define the notion of commutativity degree of crossed modules and find some bounds on commutativity degree for special types of crossed modules. Also, we give a function for finding commutativity degree of crossed modules in \textsf{GAP} and classify crossed modules by using this function.
Arvasi, Zekeriya +2 more
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