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

1a) Prove that the group (nZ, +) acts onZby a*g = a + g for all g in nZand for all a inZ.

b)What are the orbits?

c)How many orbits are there? Do the set of orbits remind you of anything in number theory?

2. Relevant equations

not sure

3. The attempt at a solution

a) For e in (nZ, +), e = 0. so a*e = a+e = a+0 = a. So the identity of (nZ, +) is also the identity onZ.

For g, h in nZ, and for a inZ, a*(g+h) = a+(g+h) = (a+g)+h = (a*g)*h.

b, c) I know what the definition of what an orbit is (here for some a inZ, O_a = {a*g = a+g | g in nZ}) I'm not sure what the question is actually asking.

For c, would the amount of orbits be equal to the amount of elements in nZ, or 2n+1?

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# Homework Help: Show the group action on (x, y) and, desribe the orbits.

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