I have to show that there are no onto homomorphisms from _ to _, including Q8 to Z4. How would I show that? Also can someone explain what onto means again, my teacher didn't explain it well to me.
How would I show that there are no onto homomorphisms from Q8 to Z4?
2
$\begingroup$
abstract-algebra
finite-groups
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0Onto means surjective: a function $\,f:A\to B\,$ is *onto* $\,B\,$ if $\forall\,b\in B\,\,\exists\,a\in A\,\,s.t.\,f(a)=b\,$ – 2012-12-14
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0Presumably (from the tag, among other hints) it's a group homomorphism at issue. What is the order of a generator of cyclic group $\mathbb{Z}_4$? – 2012-12-14