Results 141 to 150 of about 4,706 (177)
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On a lower bound of commutativity degree
Rendiconti Del Circolo Matematico Di Palermo, 2010There is a growing interest in the last years in the so-called ``commutativity degree'' of a finite group \(G\): this is defined as the number \(d(G)=\tfrac 1{|G|^2}|\{(x,y)\in G^2\mid [x,y]=1\}|\). The authors of this paper are devoting many researches in the last years to the topic, generalizing a series of recent contributions in the literature.
Rajat Kanti Nath +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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RELATIVE COMMUTATIVITY DEGREE OF A SUBPOLYGROUP OF A FINITE POLYGROUP
Journal of Mathematical ScienceszbMATH Open Web Interface contents unavailable due to conflicting licenses.
M Al Tahan, Bijan Davvaz, Davvaz B
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Commutativity degree of chains of finite groups
Journal of Discrete Mathematical Sciences & Cryptography, 2023The concepts of commutativity of two chains, and the commutativity degree of the chains of a finite group such as G which ends in G are introduced. Then, the relation between the commutativity degree of the chains of a finite group is examined, and eventually this measure is calculated for some finite groups and fuzzy subgroups.
Hamid Darabi, Mahdi Imanparast
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Non-Commuting Graphs and Some Bounds for Commutativity Degree of Finite Moufang Loops
Bulletin of the Iranian Mathematical Society, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rezaie, Elhameh +3 more
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On the commutativity degree of compact groups
Archiv Der Mathematik, 2009In any finite group \(G\), for every \(n\geq 2\) the \(n\)-th commutative degree \(d_n(G)\) is the probability that a randomly chosen ordered \((n+1)\)-tuple of the group elements is mutually commuting. The aim of this paper is to generalize this definition to every compact group, which is possible since such a group can be considered as a probability ...
Rashid Rezaei +2 more
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A NOTE ON THE RELATIVE COMMUTATIVITY DEGREE OF FINITE GROUPS
Asian-European Journal of Mathematics, 2014The purpose of this paper is to give a relation between the notion of the commutativity degree of a finite group G (denoted by d(G)) and that of isoclinism between G and an extra special p-group, where p is the smallest prime number dividing |G|.
Rezaei, Rashid, Erfanian, Ahmad
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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 Tarnauceanu
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Some results on relative commutativity degree
Rendiconti Del Circolo Matematico Di Palermo, 2015The relative commutativity degree of a subgroup \(H\) of a finite group \(G\), denoted by \(Pr(H,G)\), is the probability that an element of \(G\) commutes with an element of \(H\). The authors show some lower and upper bounds for \(Pr(H,G)\) and an invariance property of \(Pr(H,G)\) under isoclinism of pairs of groups. Even if the methods of proof may
Rajat Kanti Nath, Nath Rajat Kanti
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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.
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