On subpolygroup commutativity degree of finite polygroups
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F25%3A00560250" target="_blank" >RIV/60162694:G43__/25:00560250 - isvavai.cz</a>
Result on the web
<a href="https://www.aimspress.com/article/doi/10.3934/math.20231211" target="_blank" >https://www.aimspress.com/article/doi/10.3934/math.20231211</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/math.20231211" target="_blank" >10.3934/math.20231211</a>
Alternative languages
Result language
angličtina
Original language name
On subpolygroup commutativity degree of finite polygroups
Original language description
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. In this regard, we extend the concept of the subgroup commutativity degree of a finite group to the subpolygroup commutativity degree of a finite polygroup P. The latter measures the probability of two random subpolygroups H; K of P commuting (i.e., HK = KH). First, using the subgroup commutativity table and the subpolygroup commutativity table, we present some results related to the new defined concept for groups and for polygroups. We then consider the special case of a polygroup associated to a group. We study the subpolygroup lattice and relate this to the subgroup lattice of the base group; this includes deriving an explicit formula for the subpolygroup commutativity degree in terms of the subgroup commutativity degree. Finally, we illustrate our results via non-trivial examples by applying the formulas that we prove to the associated polygroups of some well-known groups such as the dihedral group and the symmetric group.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
AIMS MATHEMATICS
ISSN
2473-6988
e-ISSN
2473-6988
Volume of the periodical
8
Issue of the periodical within the volume
10
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
23786-23799
UT code for WoS article
001052388300016
EID of the result in the Scopus database
2-s2.0-85167423194