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Representants of cosets

function Representants(cosets::Set{Set{Elt}})::Dict{Elt,Elt}
repr = Dict{Elt,Elt}()
for s in cosets
r = minimum(s) # FIXME To make the set of representants a SubGroup
for e in s
push!(repr, e => r)
end
end
return repr
end

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.

Git good practices

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 Type

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.

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