Syrbu, ParascoviaCeban, Dina2016-04-012016-04-012014SYRBU, P., CEBAN, D. On π-quasigroups of typeT1. In: Buletinul Academiei de Ştiinţe a Republicii Moldova : Matematica. 2014, nr. 2(75), pp. 36-431024-7696https://msuir.usm.md/handle/123456789/580https://doaj.org/toc/1024-7696Quasigroups satisfying the identityx(x· xy ) = y are called π -quasigroups of type T 1 . The spectrum of the defining identity is precisely q = 0 or 1(mod 3), except for q = 6. Necessary conditions when a finite π -quasigroup of type T 1 has the order q = 0 (mod 3), are given. In particular, it is proved that a finite π -quasigroup of type T 1 such that the order of its inner mapping group is not divisible by three has a left unit. Necessary and sufficient conditions when the identityx ( x · xy ) = y is invariant under the isotopy of quasigroups (loops) are foundenMinimal identityπ -quasigroup of type T 1spectruminvariants under isotopyArticle