On subpolygroup commutativity degree of finite polygroups

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On subpolygroup commutativity degree of finite polygroups

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On subpolygroup commutativity degree of finite polygroups

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

AIMS MATHEMATICS

ISSN

2473-6988

e-ISSN

2473-6988

Svazek periodika

8

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

23786-23799

Kód UT WoS článku

001052388300016

EID výsledku v databázi Scopus

2-s2.0-85167423194