ON QUASIGROUPS WITH SOME MINIMAL IDENTITIESON QUASIGROUPS WITH SOME MINIMAL IDENTITIES

Dina CEBAN, Parascovia SYRBU Moldova State University

Аннотация

Quasigroups with two identities (of types and ) from Belousov-Bennett classification are considered. It is proved that a -quasigroup of type is also of type if and only if it satisfies the identity (the “right keys law”), so -quasigroups that are of both types and are -quasigroups. Also, it is proved that -quasigroups of type are isotopic to idempotent quasigroups. Necessary and sufficient conditions when a -quasigroup of type is isotopic to a group (an abelian group) are found. It is shown that the set of all -quasigroups of type isotopic to abelian groups is a subvariety in the variety of all -quasigroups of type and that - -quasigroups of type are medial quasigroups. Using the symmetric group on , some considerations for the spectrum of finite -quasigroups of type are discussed. Keywords: minimal identities, -quasigroup, group’s isotopes, spectrum.