On quasi-ideals of semirings.
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.
A subgroup of a finite group is said to be conjugate-permutable if for all . More generaly, if we limit the element to a subgroup of , then we say that the subgroup is -conjugate-permutable. By means of the -conjugate-permutable subgroups, we investigate the relationship between the nilpotence of and the -conjugate-permutability of the Sylow subgroups of and under the condition that , where and are subgroups of . Some results known in the literature are improved and...