On some varieties of abelian quasigroups

The primitive quasigroups isotopic to groups form a variety characterised by one identity. Previously G. B. Belyavskaya and the author showed that the variety of all primitive Abelian quasigroups ($T$-quasigroups) can be characterised by three identities. In this paper, we consider a subvariety of Abelian quasigroups and prove that it can be characterised by one of two identities.