def test_center():
# the center of the dihedral group D_n is of order 2 for even n
for i in (4, 6, 10):
D = DihedralGroup(i)
assert (D.center()).order() == 2
# the center of the dihedral group D_n is of order 1 for odd n>2
for i in (3, 5, 7):
D = DihedralGroup(i)
assert (D.center()).order() == 1
# the center of an abelian group is the group itself
for i in (2, 3, 5):
for j in (1, 5, 7):
for k in (1, 1, 11):
G = AbelianGroup(i, j, k)
assert G.center().is_subgroup(G)
# the center of a nonabelian simple group is trivial
for i in (1, 5, 9):
A = AlternatingGroup(i)
assert (A.center()).order() == 1
# brute-force verifications
D = DihedralGroup(5)
A = AlternatingGroup(3)
C = CyclicGroup(4)
G.is_subgroup(D * A * C)
assert _verify_centralizer(G, G)
def test_center():
# the center of the dihedral group D_n is of order 2 for even n
for i in (4, 6, 10):
D = DihedralGroup(i)
assert (D.center()).order() == 2
# the center of the dihedral group D_n is of order 1 for odd n>2
for i in (3, 5, 7):
D = DihedralGroup(i)
assert (D.center()).order() == 1
# the center of an abelian group is the group itself
for i in (2, 3, 5):
for j in (1, 5, 7):
for k in (1, 1, 11):
G = AbelianGroup(i, j, k)
assert G.center().is_subgroup(G)
# the center of a nonabelian simple group is trivial
for i in(1, 5, 9):
A = AlternatingGroup(i)
assert (A.center()).order() == 1
# brute-force verifications
D = DihedralGroup(5)
A = AlternatingGroup(3)
C = CyclicGroup(4)
G.is_subgroup(D*A*C)
assert _verify_centralizer(G, G)
