- #1
tomkoolen
- 40
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Member warned about posting without the template
Hello, I have to solve the following problem:
Show that a homomorphism from a finite group G to Q, the additive group of rational numbers is trivial, so for every g of G, f(g) = 0.
My work so far:
f(x+y) = f(x)+f(y)
I know that |G| = |ker(f)||Im(f)|
I think that somehow I have to find that Im(f) = 1 but I don't know how. Can anybody help me please?
Thanks in advance!
Show that a homomorphism from a finite group G to Q, the additive group of rational numbers is trivial, so for every g of G, f(g) = 0.
My work so far:
f(x+y) = f(x)+f(y)
I know that |G| = |ker(f)||Im(f)|
I think that somehow I have to find that Im(f) = 1 but I don't know how. Can anybody help me please?
Thanks in advance!