Congruences of finite multi-base universal algebras isomorphic to $n$-ary groups derived from groups

The homomorphism of a multi-base universal algebra to a multi-base universal algebra will be called an $mb$-homomorphism, and the corresponding congruences will be called $mb$-congruences. A description is obtained of $mb$-congruences of finite multi-base universal algebras, $mb$-isomorphic to $n$-ary groups derived from groups, that is, admitting representation in the form of a sequential application of the operation of some group. In particular, this class includes universal algebras for which the Gluskin – Hosszu theorem and its analogues are valid for $n$-ary operations.