On permutable N-groups
Some properties of quasigroups with the left loop property are investigated. In loops we point out that the left loop property is closely related to the left Bol identity and the particular case of homogeneous loops is considered.
In this part the smallest non-abelian quasivarieties for nilpotent Moufang loops are described.
In this part of the paper we study the quasiidentities of the nilpotent Moufang loops. In particular, we solve the problem of finite basis for quasiidentities in the finitely generated nilpotent Moufang loop.
Properties of -ary groups connected with the affine geometry are considered. Some conditions for an -ary -group to be derived from a binary group are given. Necessary and sufficient conditions for an -ary group -derived from an additive group of a field to be an -group are obtained. The existence of non-commutative -ary -groups which are not derived from any group of arity for every , is proved.