Gyrogroups and the Cauchy property
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2024-02-28 10:54
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517.98 (48)
Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (241)
SM ISO690:2012
SUKSUMRAN, Teerapong, UNGAR, Abraham. Gyrogroups and the Cauchy property. In: Quasigroups and Related Systems, 2016, vol. 24, nr. 2(36), pp. 277-286. ISSN 1561-2848.
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Quasigroups and Related Systems
Volumul 24, Numărul 2(36) / 2016 / ISSN 1561-2848

Gyrogroups and the Cauchy property
CZU: 517.98

Pag. 277-286

Suksumran Teerapong1, Ungar Abraham2
 
1 Chulalongkorn University,
2 North Dakota State University
 
Disponibil în IBN: 10 martie 2017


Rezumat

A gyrogroup is a nonassociative group-like structure. In this article, we extend the Cauchy property from groups to gyrogroups. The (weak) Cauchy property for _nite gyrogroups states that if p is a prime dividing the order of a gyrogroup G, then G contains an element of order p. An application of a result in loop theory shows that gyrogroups of odd order as well as solvable gyrogroups satisfy the Cauchy property. Although gyrogroups of even order need not satisfy the Cauchy property, we prove that every gyrogroup of even order contains an element of order two. As an application, we prove that every group of order nq, where n 2 N and q is a prime with n < q, contains a unique characteristic subgroup of order q.

Cuvinte-cheie
Cauchy's theorem,

gyrogroup, Bol loop