Question

Show that { (1), (123), (132) } Is a subgroup of S_3. And why is { (1), (12), (23), (13) } not a subgroup of S_3?

Answer 1

show the first set is closed under mult

for the 2nd compute (12)(23)

Answer 2

notice that (123) and (132) are inverses. and that (123)^2=(132) and (132)^2=(123)