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.
In the last two sections the authors like to discuss priority issues.


20N05 Loops, quasigroups
22A30 Other topological algebraic systems and their representations


Zbl 0799.20032
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