Sabinin, Lev V.; Sabinina, Ludmila L.; Sbitneva, Larissa V. On the notion of gyrogroup. (English) Zbl 0923.20051 Aequationes Math. 56, No. 1-2, 11-17 (1998). It is shown that a set of axioms for gyrogroups [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. Reviewer: H.Kiechle (Hamburg) Cited in 1 ReviewCited in 24 Documents MSC: 20N05 Loops, quasigroups 22A30 Other topological algebraic systems and their representations Keywords:loops; gyrogroups; Bol identity; Bruck loops; K-loops; Bol loops; inner mappings Citations:Zbl 0799.20032 PDFBibTeX XMLCite \textit{L. V. Sabinin} et al., Aequationes Math. 56, No. 1--2, 11--17 (1998; Zbl 0923.20051) Full Text: DOI