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On the notion of gyrogroup. (English) Zbl 0923.20051
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.
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##### MSC:
 20N05 Loops, quasigroups 22A30 Other topological algebraic systems and their representations
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