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Math Help - homomorphism

  1. #1
    Junior Member
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    homomorphism

    Show that f(x,y)=x(-1)^y is homomorphism from the direct product group (positive) ×2 to the group *.

    (need to show that f((a,b)(c,d))=f(a,b)f(c,d), is it right? but I can't get them equal to each other)
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  2. #2
    Super Member
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    Take (a,b),(c,d)\in \mathbb{R}^+ \times \mathbb{Z}_2 then f((a,b)(c,d))=ac(-1)^{b+d}=ac(-1)^b(-1)^d=a(-1)^bc(-1)^d=f((a,b))f((c,d))

    I'm assuming \mathbb{R} ^+ is the group of postitive real numbers with multiplication as operation.
    Last edited by Jose27; November 21st 2009 at 10:49 PM.
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