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Math Help - Q, S3 and homomorphism

  1. #1
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    [SOLVED] Q, S3 and homomorphism

    Q, S3 and homomorphism-number-8.png


    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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  2. #2
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    Re: Q, S3 and homomorphism

    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 S3 of order 4, but 4 does not divide 6.
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