def test_derived_series(): # the derived series of the trivial group consists only of the trivial group triv = PermutationGroup([Permutation([0, 1, 2])]) assert triv.derived_series()[0].is_subgroup(triv) # the derived series for a simple group consists only of the group itself for i in (5, 6, 7): A = AlternatingGroup(i) assert A.derived_series()[0].is_subgroup(A) # the derived series for S_4 is S_4 > A_4 > K_4 > triv S = SymmetricGroup(4) series = S.derived_series() assert series[1].is_subgroup(AlternatingGroup(4)) assert series[2].is_subgroup(DihedralGroup(2)) assert series[3].is_trivial
def test_derived_series(): # the derived series of the trivial group consists only of the trivial group triv = PermutationGroup([Permutation([0, 1, 2])]) assert triv.derived_series()[0].is_subgroup(triv) # the derived series for a simple group consists only of the group itself for i in (5, 6, 7): A = AlternatingGroup(i) assert A.derived_series()[0].is_subgroup(A) # the derived series for S_4 is S_4 > A_4 > K_4 > triv S = SymmetricGroup(4) series = S.derived_series() assert series[1].is_subgroup(AlternatingGroup(4)) assert series[2].is_subgroup(DihedralGroup(2)) assert series[3].is_trivial