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Subgroups with large relative commutativity degree

Quaestiones Mathematicae, 2017
The order of subgroups with large relative commutativity degrees are determined. Also a relationship between the number of relative commutativity degrees of a group and the length of its subgroup chains is obtained.Mathematics Subject Classication (2010):
Hesam Safa
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SEMIGROUPS WITH MAXIMUM COMMUTING REGULARITY DEGREE

JP Journal of Algebra, Number Theory and Applications, 2017
Summary: 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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Neighbors Degree Sum Energy of Commuting and Non-Commuting Graphs for Dihedral Groups

Malaysian Journal of Mathematical Sciences, 2023
The 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 NDS−matrix 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 degree of commutativity of p-groups of maximal class [PDF]

Journal of Pure and Applied Algebra, 2011
The first major study of p-groups of maximal class was made by Blackburn in 1958. He showed that an important invariant parameter of these groups is its ‘degree of commutativity’, which is a measure of the commutativity among the members of the lower ...
A Vera-López
exaly   +2 more sources

Commutativity degree of chains of finite groups

Journal of Discrete Mathematical Sciences & Cryptography, 2023
The 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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A NOTE ON THE RELATIVE COMMUTATIVITY DEGREE OF FINITE GROUPS

Asian-European Journal of Mathematics, 2014
The 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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Finite Groups with Four Relative Commutativity Degrees

Algebra Colloquium, 2015
It is shown that a finite group G has four relative commutativity degrees if and only if G/Z(G) is a p-group of order p3 and G has no abelian maximal subgroups, or G/Z(G) is a Frobenius group with Frobenius kernel and complement isomorphic to ℤp × ℤp and ℤq, respectively, and the Sylow p-subgroup of G is abelian, where p and q are distinct primes.
Erfanian, A., Farrokhi D. G., M.
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Methods for Computing the Concurrency Degree of Commutation Monoids

2000
Mazurkiewicz proposed trace monoids to model syntactically concurrent processes. A commutation system is an action alphabet A together with a binary relation θ. Whenever (a, b) ∈ θ, the actions a and b are not causally related and, therefore, they are allowed to commute.
Saheb-Djahromi, Nasser, Zemmari, Akka
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Degree four identities not implied by commutativity

Communications in Algebra, 1988
We classify all (reducible or irreducible) degree four identities not implied by commutativlty, thus extending [1]. We study one class under the presence of an idempotent. For almost all the algebras of this class, simplicity implies associativity; we find, however, a generalization of right alternativity which contains significant algebras, including ...
CARINI, Luisa, I. R. HENTZEL, G. M. PIACENTINI CATTANEO   +2 more
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Subpolygroup commutativity degree of finite extension polygroup

International Journal of Algebra and Computation
In this paper, we consider finite extension polygroups as a special class of polygroups to study probabilistic polygroup theory. In this regard, we study the subpolygroup lattice of the extension polygroups. By using the results of the subpolygroup lattice, we obtain an explicit formula for the subpolygroup commutativity degree of the extension ...
Madeleine Al-Tahan, Bijan Davvaz, P. Harikrishnan, Pallavi Pallavi   +3 more
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