def test_composition_series():
a = Permutation(1, 2, 3)
b = Permutation(1, 2)
G = PermutationGroup([a, b])
comp_series = G.composition_series()
assert comp_series == G.derived_series()
# The first group in the composition series is always the group itself and
# the last group in the series is the trivial group.
S = SymmetricGroup(4)
assert S.composition_series()[0] == S
assert len(S.composition_series()) == 5
A = AlternatingGroup(4)
assert A.composition_series()[0] == A
assert len(A.composition_series()) == 4
# the composition series for C_8 is C_8 > C_4 > C_2 > triv
G = CyclicGroup(8)
series = G.composition_series()
assert is_isomorphic(series[1], CyclicGroup(4))
assert is_isomorphic(series[2], CyclicGroup(2))
assert series[3].is_trivial
