Homomorphic embeddings in n-groups

We prove that an cancellative n-groupoid A can be homotopic embedded in an n-group if and only if in A are satis ed all n-ary Malcev conditions. Now we shall prove that in the presence of associative law we obtain homomorphic embeddings. Furthermore, if A has a lateral identity a such embeddings is assured by a subset of n-ary Malcev conditions - unary Malcev conditions.