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Coset's representant is actually the minimum for lexical order but nothing is done to check if the set of these representants is a valid subGroup. Instead, a dictionary is used and it is not a great option, particulary for internal direct product with another subgroup. Finding an example that throw exception for this issue will be a good progress in studying finite group subject.

Committing often, for each modification on a file or across multiple file with a significative message to make commit report easy to read and to understand.

Abstract Groups are ambiguous. A primitive element is always user-defined related to a primitive user-defined group. Other computational groups are manipulating primitives elements or a tuple of primitive elements. Their base group is always the same of the neutral element base group which is at least the first requirement for their creation.

Current code works but it doesnt takes full benefits from Julia.

The code need a great refactoring before adding any other new functions.