GroupsWithPropertyT/groups/autfreegroup.jl

struct SpecialAutomorphismGroup{N} <: SymmetrizedGroup
    group::AutGroup
end

function SpecialAutomorphismGroup(args::Dict)
    N = args["SAut"]
    return SpecialAutomorphismGroup{N}(AutGroup(FreeGroup(N), special=true))
end

name(G::SpecialAutomorphismGroup{N}) where N = "SAutF$(N)"

group(G::SpecialAutomorphismGroup) = G.group

function generatingset(G::SpecialAutomorphismGroup)
    S = gens(group(G));
    return unique([S; inv.(S)])
end

function autS(G::SpecialAutomorphismGroup{N}) where N
    return WreathProduct(PermutationGroup(2), PermutationGroup(N))
end