Results 111 to 120 of about 441 (146)
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On the commutativity degree of a group algebra
Afrika Matematika, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdollah Chashiani, Rashid Rezaei
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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.
Nath, Rajat Kanti, Das, Ashish Kumar
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SEMIGROUPS WITH MAXIMUM COMMUTING REGULARITY DEGREE
JP Journal of Algebra, Number Theory and Applications, 2017Summary: The commuting regularity degree, \(\mathrm{dcr}(S)\) of a non-group semigroup \(S\) is defined and studied recently by the authors [Creat. Math. Inform. 24, No. 1, 43--47 (2015; Zbl 1349.20044)], where \(\mathrm{dcr}(S)\) is the probability that a pair \((x,y)\) of the elements of \(S\) is a commuting regular pair (the pair \((x,y)\) is called
Firuzkuhy, A., Doostie, H.
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Some results on relative commutativity degree
Rendiconti del Circolo Matematico di Palermo (1952 -), 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
Nath, Rajat Kanti, Yadav, Manoj Kumar
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Isoclinism Classes and Commutativity Degrees of Finite Groups
Journal of Algebra, 1995 Let \(G\) be a finite group, and for \(n\geq 0\), define \[ d_n(G)=|G|^{-(n+1)}|\{(x_1,\dots,x_{n+1})\in G^{n+1}\mid[x_i,x_j]=1,\;1\leq i,j\leq n+1\}|. \] So, \(d_1(G)=d(G)\) is the probability that two elements chosen randomly from \(G\) (with replacement) commute [see the reviewer, Am. Math. Mon. 80, 1031-1034 (1973; Zbl 0276.60013)].
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Neighbors Degree Sum Energy of Commuting and Non-Commuting Graphs for Dihedral Groups
Malaysian Journal of Mathematical Sciences, 2023The neighbors degree sum (NDS) energy of a graph is determined by the sum of its absolute eigenvalues from its corresponding neighbors degree sum matrix. The non-diagonal entries of NDSâmatrix are the summation of the degree of two adjacent vertices, or it is zero for non-adjacent vertices, whereas for the diagonal entries are the negative of the ...
Romdhini, M. U., Nawawi, A., Chen, C. Y.
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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 ...
Rezaei, Rashid, Erfanian, Ahmad
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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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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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