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The Class Equation and the Commutativity Degree for Complete Hypergroups [PDF]

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
doaj   +5 more sources

Factorization number and subgroup commutativity degree via spectral invariants [PDF]

Computational and Applied Mathematics, 2023
The factorization number $$F_2(G)$$ F 2 ( G ) of a finite group G is the number of all possible factorizations of $$G=HK$$ G = H K as a product of its subgroups H and K , while the subgroup commutativity degree $$\textrm{sd}(G)$$ sd ( G ) of G is the ...
Seid Muhie, Daniele Ettore Otera, Francesco G Russo   +2 more
exaly   +4 more sources

On Commutativity Degree of Crossed Modules [PDF]

Kragujevac Journal of Mathematics
In this paper, we define and study the notion of commutativity degree of finite crossed modules. We shall state some results concerning commutativity degree of crossed modules and obtain some upper and lower bounds for commutativity degree of finite crossed modules.
SOMAYEH AMINI, Shahram Heidarian, FARHAD KHAKSAR HAGHANI   +2 more
semanticscholar   +4 more sources

The degree of commutativity of wreath products with infinite cyclic top group [PDF]

European Journal of Mathematics, 2022
The degree of commutativity of a finite group is the probability that two uniformly and randomly chosen elements commute. This notion extends naturally to finitely generated groups G: the degree of commutativity $${{\,\textrm{dc}\,}}_S(G)$$
Iker de las Heras, Benjamin Klopsch, Andoni Zozaya   +2 more
exaly   +4 more sources

Subgroup S-commutativity degrees of finite groups [PDF]

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2012
The so--called subgroup commutativity degree $sd(G)$ of a finite group $G$ is the number of permuting subgroups $(H,K) \in \mathrm{L}(G) \times \mathrm{L}(G)$, where $\mathrm{L}(G)$ is the subgroup lattice of $G$, divided by $|\mathrm{L}(G)|^2$. It allows us to measure how $G$ is far from the celebrated classification of quasihamiltonian groups of K ...
Francesco G Russo
exaly   +8 more sources

Graph Related to Cubed Commutativity Degree

ASM Science Journal, 2020
Graph Related to Cubed Commutativity Degree N. M. Mohd Ali1*, M. Abdul Hamid2, N. H. Sarmin1 and A. Erfanian3 1Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia 2Faculty of ...
Nik Ahmad Ridhwan Nik Mohd, Muhammad Fareed Hamid, Nor Haniza Sarmin, Ahmad Erfanian, A Abdollahi, S Akbari, H Maimani, E Bertram, M Herzog, A Mann, M Bianchi, D Chillag, A Mauri, M Herzog, C Scoppola, M Bianchi, M Herzog, E Pacifici, G Saffirio, D Chillag, M Herzog, A Mann, M El-Sanfaz, N Sarmin, A Erfanian, B Tolue, A Erfanian, B Tolue, A Moreto, G Qian, W Shi, S Omer, N Sarmin   +32 more
semanticscholar   +4 more sources

Energetic formulation of the subgroup commutativity degree

Nonlinear Analysis
Finite 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, Daniele Ettore Otera, Francesco G. Russo   +2 more
doaj   +4 more sources

On subpolygroup commutativity degree of finite polygroups

AIMS Mathematics, 2023
<abstract><p>Probabilistic group theory is concerned with the probability of group elements or group subgroups satisfying certain conditions. On the other hand, a polygroup is a generalization of a group and a special case of a hypergroup. This paper generalizes probabilistic group theory to probabilistic polygroup theory.
M. Al Tahan, Sarka Hoskova-Mayerova, B. Davvaz, A. Sonea   +3 more
exaly   +4 more sources

The cubed commutativity degree of dihedral groups [PDF]

AIP Conference Proceedings, 2016
Let G be a finite group. The commutativity degree of a group is the probability that a random pair of elements in the group commute. Furthermore, the n-th power commutativity degree of a group is a generalization of the commutativity degree of a group which is defined as the probability that the n-th power of a random pair of elements in the group ...
Muhanizah Abdul Hamid, Nor Muhainiah Mohd Ali, Nor Haniza Sarmin, Ahmad Erfanian   +3 more
semanticscholar   +3 more sources

On asymptotic commutativity degree of finite groups

Proyecciones (Antofagasta), 2019
The aim of this paper is to give a detailed account of a problema posed by P. Lescot regarding asymptotic commutativity degree of finite groups.
Rajat Kanti Nath
semanticscholar   +6 more sources