On the notion of gyrogroup (Q1271575)

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.