On the notion of gyrogroup
type: Item
instance of: scholarly article
title: On the notion of gyrogroup
zbMATH Open document ID: 0923.20051
author: L. V. Sabinin
author: Liudmila Sabinina
author: Larissa V. Sbitneva
published in: Aequationes Mathematicae
publication date: 1999-02-14T00:00:00Z
review text: It is shown that a set of axioms for gyrogroups [\textit{A. A. Ungar}, Aequationes Math. 47, No. 2-3, 240-254 (1994; Zbl 0799.20032)] is equivalent to the axioms for Bol loops with automorphic inverse property, i.e., K-loops or Bruck loops. In particular, it is proved that the identity \(\ell(xy,y)=\ell(x,y)\) for left inner mappings is equivalent to the Bol identity. In the last two sections the authors like to discuss priority issues.
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 22A30
zbMATH DE Number: 1220992
zbMATH Keywords: loops
zbMATH Keywords: gyrogroups
zbMATH Keywords: Bol identity
zbMATH Keywords: Bruck loops
zbMATH Keywords: K-loops
zbMATH Keywords: Bol loops
zbMATH Keywords: inner mappings
reviewed by: Hubert Kiechle
MaRDI profile type: Publication
full work available at URL: s000100050039
OpenAlex ID: W2095442691
DOI: 10.1007/S000100050039
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description: scientific article; zbMATH DE number 1220992