SOLVED. It was quite easy and straight-forward. Sorry for the useless post.
Last edited by bondvalencebond; December 15th 2012 at 12:55 PM.
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it's not. we see that φ(ij) = φ(k) = (2 3), whereas: φ(i)φ(j) = (1 2)(1 3) = (1 3 2) ≠ (2 3). **************** alternatively, if φ WAS a homomorphism, then φ(Q) would be a subgroup of S_{3} of order 4, but 4 does not divide 6.
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