- #1
Demon117
- 165
- 1
If you have the dihedral group D4 and the symmetric group S8 how do you come up with a 1-to-1 group homomorphism from D4 to S8. I know what the multiplication table looks like. How can I use that to create the homomorphism?
Let R1,. . . ., R4 represent the rotation symmetry. Let u1, u2 represent the cross-sectional symmetries, and d1,d2 represents the diagonal symmetries.
A group homomorphism must take the form that for a,b in D4
(ab)phi = (a*phi)(b*phi)
But this is elusive notation. What does it mean and how can I proceed? An example to work off of similar to this would be great!
Let R1,. . . ., R4 represent the rotation symmetry. Let u1, u2 represent the cross-sectional symmetries, and d1,d2 represents the diagonal symmetries.
A group homomorphism must take the form that for a,b in D4
(ab)phi = (a*phi)(b*phi)
But this is elusive notation. What does it mean and how can I proceed? An example to work off of similar to this would be great!