Hey -- if anyone out there in TWW land are also working on this problem, but I'll throw it out.

Well, two questions I guess. First is Prove that a factor group of a cyclic group is cyclic. Obviously I know what a cyclic group is, but I don't know how to incorporate that into the factor group.

The second question is what is the order of 14 + <8> in the factor group Z_24 / <8>. I know that Z_24 / <8> becomes ... Z_6 (?), but I'm not sure how.

Thanks for any help you can throw my way..

4/2/2006 2:33:30 PM

oh god... so long ago

don't you have a book?

it's going to give you as good of help as anyone here

4/2/2006 3:45:09 PM

too easy.

I'll help you on the first.

Look at how you proved the group axioms of G/N and think about what it means to be cyclic. Then apply the cyclic properties of G.

4/2/2006 4:26:39 PM

^ yep. Like he said remember that for a cyclic group we know how to explicitly write each and every element in terms of the generator raised to some power (0,1,2,3,...,g -1). For a cyclic group G of order g we knows:

G = {e,a,a^2,a^3,...A^g-1} with a^g=e

or if you like,

G = {0,a,2a,3a,...(g-1)a} with ga= 0

I suppose you'll want to think about additive groups in view of the problem to follow.

[Edited on April 2, 2006 at 4:42 PM. Reason : formatting]

4/2/2006 4:41:16 PM