zcahana
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Homework Statement
The exercise is to find examples of various homomorphisms from/to various groups.
Those I'm having problems with are:
a. f: (Q,+) --> (Q^+,*) which is onto.
b. f: U20 --> Z64 which is 1-to-1.
c. f: Z30 --> S10 which is 1-to-1.
Homework Equations
The Attempt at a Solution
for a. , the only homomorphism i could think which send 0 to 1 is f(x) a^x,
apparently, f sends many elements of (Q,+) to R instead of (Q^+,*).
for b. , the only insight i have is that U20 has 8 elements, and Z64 has 8*8 elements ... not to deep, i know ... but maybe is?
for c. , no insights at all.
I would appreciate any clues given.
Thanks,
Zvi.