- #1

LCSphysicist

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Hello everyone. I have been study a little of group theory, i am a little stuck in how to answer question like this:

"How many homomorphism #f: S_{3}\to Q_{8}# are there? $S_{3}$ and $Q_8$ are the permutations group and the quaternion group, respectively."

A homomorphism is a map from A to B such that $\phi(a') \phi(a'') = \phi(a' a '')$, but how to apply this definition to answer the question?

I could construct the multiplicative table for $Q_{8}$, maybe call i j k 1 -i -j -k -1 as 1 2 3 ... 8, but yet have no idea what to do. Maybe seek a "little table" inside this modified table of Q8 that looks like S3?

"How many homomorphism #f: S_{3}\to Q_{8}# are there? $S_{3}$ and $Q_8$ are the permutations group and the quaternion group, respectively."

A homomorphism is a map from A to B such that $\phi(a') \phi(a'') = \phi(a' a '')$, but how to apply this definition to answer the question?

I could construct the multiplicative table for $Q_{8}$, maybe call i j k 1 -i -j -k -1 as 1 2 3 ... 8, but yet have no idea what to do. Maybe seek a "little table" inside this modified table of Q8 that looks like S3?