On loop extensions and cohomology of loops

In this paper are defined cohomology-like groups that classify loop extensions satisfying a given identity in three variables for association identities, and in two variables for the case of commutativity. It is considered a large amount of identities. This groups generalize those defined in works of Nishigori [2] and of Jhonson and Leedham-Green [4]. It is computed the number of metacyclic extensions for trivial action of the quotient on the kernel in one particular case for left Bol loops and in general for commutative loops.