On $\pi$-quasigroups isotopic to abelian groups

A $\pi$-quasigroup is a quasigroup satisfying one of the seven minimal identities from the V. Belousov's classification given in [1]. Some general results about $\pi$-quasigroups isotopic to groups are obtained by V. Belousov and A. Gwaramija in [1] and [2]. $\pi$-Quasigroups isotopic to abelian groups are investigated in this paper.