def test_lower_central_series(): # the lower central series of the trivial group consists of the trivial # group triv = PermutationGroup([Permutation([0, 1, 2])]) assert triv.lower_central_series()[0].is_subgroup(triv) # the lower central series of a simple group consists of the group itself for i in (5, 6, 7): A = AlternatingGroup(i) assert A.lower_central_series()[0].is_subgroup(A) # GAP-verified example S = SymmetricGroup(6) series = S.lower_central_series() assert len(series) == 2 assert series[1].is_subgroup(AlternatingGroup(6))
def test_lower_central_series(): # the lower central series of the trivial group consists of the trivial # group triv = PermutationGroup([Permutation([0, 1, 2])]) assert triv.lower_central_series()[0].is_subgroup(triv) # the lower central series of a simple group consists of the group itself for i in (5, 6, 7): A = AlternatingGroup(i) assert A.lower_central_series()[0].is_subgroup(A) # GAP-verified example S = SymmetricGroup(6) series = S.lower_central_series() assert len(series) == 2 assert series[1].is_subgroup(AlternatingGroup(6))