Simple project concerning finite groups...
Example:
julia> using FiniteGroups
julia> σ = Cyc(1,2,3)
(2,3,1)
julia> map(σ, 2)
3
julia> τ = Permutation(1 => 2, 2 => 1, 3 => 4, 4 => 5, 5 => 3)
(5,3,4)(2,1)
julia> σ*τ
(5,1,3,4)
julia> (σ*τ)^-1 == τ^-1*σ^-1
true
julia> G = Group(σ, τ)
Finite permutation group with 2 generators ..
julia> orbit(G, 1)
5-element Vector{Int64}:
1
2
3
4
5
julia> elements(G)
120-element Vector{Any}:
()
(2,3,1)
(5,3,4)(2,1)
(2,1,3)
(5,3,2,4)
(5,1,3,4)
(5,4,3)
(5,3,1,4)
(5,1,2,4)
(5,4,3,1,2)
⋮
(5,4)(2,1,3)
(5,3,2)(4,1)
(4,3)(2,1)
(5,2)(3,1)
(4,3,2)
(5,3,4,1)
(5,1,3)
(4,3,1)
(5,4)