Recent content by Jupiter

Isn't this the only kind of group I could possibly mean?

finitely generated group To be honest, I don't know of any other kind of "finitely generated" so I took it for granted that I meant groups.

I think I've got a proof. Let X=\{\frac{a_1}{b_1},\frac{a_2}{b_2},...,\frac{a_n}{b_n}\}\subset \mathbb{Q}. Consider \langle \frac{1}{b_1b_2...b_n}\rangle. Then if x\in \langle X\rangle , we know x=\frac{c_1a_1}{b_1}+\frac{c_2a_2}{b_2}+...+\frac{c_na_n}{b_n} for some c_i\in \mathbb{Z}. It...

Can someone guide me through the proof (or point me to where I can find the proof) that the group of rational numbers is not finitely generated? I know that it helps to break it into steps, the first of which you show that any finitely generated subgroup of Q is contained in a cyclic subgroup...

I got it! I needed part b. I was going about the problem the wrong way. Thanks anyway!

How can I show that if \frac{a}{a^2-2b^2},\frac{b}{a^2-2b^2}\in \mathbb{Z} then a^2-2b^2=\pm 1? If you care to see the whole problem, you can find it here: http://www.math.rochester.edu/courses/236H/home/hw12.pdf It's #4 part c. BTW, why is the significance of this "norm map"? I...

I meant the multiphoton effect. I'm having difficulty with finding articles on the multiphoton effect that explain it at a sufficiently elementary level that I can understand.

Zapper, do you know who wrote the pioneering papers on this topic? When was this phenomenon discovered, etc?

Hi Zapper. That idea is right along the lines I need. It sounds like a perfect fit to what the professor wants. I will suggest it to my professor (I need his approval). Thanks for offering to help me with the project. The paper is due May 7, so it's not crucial if you're gone one weekend...

I have to write an 8-10 page paper for my modern physics class. I was hoping someone here with more experience could suggest an interesting and accessible topic. The paper is going to have to be pretty long, so I'm going to have to be able to study this topic without getting severely lost in...

13) Find the 3rd derivative y = 8x^2 - 4x + 7 3rd derivative does not exist because highest power is 2. third derivative does exist - it's just 0 y'=16x-4 y''=16 y'''=0

Hence if we have any two permutations (with the same cycle type) whose "total length" is less than n-1, these two cycles are conjugate in A_n. However, it is quite discouraging to try to compute the size of the conjugacy class for permutations other than these types. I tried doing it for...

Is it correct to say that if you conjugate a k-cycle by a 2-cycle, then the entries in that are in the 2-cycle are swapped in the k-cycle? For example, (34)(2345)(34)=(2435) (13)(1436)(13)=(3416) (13)(4365)(13)=(4165) This is a very useful observation! Now I know if I conjugate a k-cycle...

.....ok, how about this, what's an odd permutation?

Ok, so I guess I know it's too much to ask, but I just learned how to classify all finite abelian groups, so I figured the next step was to ask what we can know about nonabelian groups. Concerning matt grime's comment that any two groups of order p^2 are isomorphic, I was under the impression...