- #1
cmj1988
- 23
- 0
Given a subgroup of G=S3={(1)(2)(3), (1 2)(3)} acting on the set S3 defined as g in G such that gxg-1 for every x in S3. Describe the orbit.
The first one is (1)(2)(3)x(3)(2)(1). This orbit is just the identity.
For the second one, I'm not sure how to describe (1 2)(3) except by multiplying it out.
(1 2)(3)(1)(2)(3)(2 1)(3) = (1)(2)(3)
(1 2)(3)(1 2)(2 1)(3) = (1 2)(3)
(1 2)(3)(1 3)(2 1)(3) = (1)(3 2)
(1 2)(3)(2 3)(2 1)(3) = (1 3)(2)
(1 2)(3)(1 2 3)(2 1)(3) = ?
(1 2)(3)(1 3 2)(2 1)(3) = ?
The first one is (1)(2)(3)x(3)(2)(1). This orbit is just the identity.
For the second one, I'm not sure how to describe (1 2)(3) except by multiplying it out.
(1 2)(3)(1)(2)(3)(2 1)(3) = (1)(2)(3)
(1 2)(3)(1 2)(2 1)(3) = (1 2)(3)
(1 2)(3)(1 3)(2 1)(3) = (1)(3 2)
(1 2)(3)(2 3)(2 1)(3) = (1 3)(2)
(1 2)(3)(1 2 3)(2 1)(3) = ?
(1 2)(3)(1 3 2)(2 1)(3) = ?