(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: A few examples of group homomorphism

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