Recent content by lostNfound

Right. I understand that the subset of complex numbers shown is a group under multiplication, and I know that it itself is cyclic with i and -i both being generators, but I know it isn't expressed as an external direct product of cyclic groups.

I'm wondering if anyone can help me with learning how to write groups as an external direct product of cyclic groups. The example I'm looking at is for the subset {1, -1, i, -i} of complex numbers which is a group under complex multiplication. How do I express it as an external direct...

If you're asking what the determinant of the inverse matrix is, then it is 1/(ad-bc).

So in describing the elements of M2(Z) that have multiplicative inverses, the answer that I keep coming back to is that the only ones are those with determinants of +/- 1, because the determinant would have to be able to divide all elements. I think I've conifrmed this scouring the web, but...

That helps a lot. I'm not sure why I didn't look at it that way before but now I know what was meant by the question. Thanks! I'll let you know if for some reason I get stuck again.

So the problem has to deal with Mersenne numbers 2^p-1 where p is a odd prime, and Mp may or may not end up being prime. The theorem given is: If p is an odd prime, but Mp=2^p-1 is not a Mersenne prime, then every divisor of the Mersenne number 2^p-1 is of the form 2*c*p+1 where c is a...

Sorry I deleted that. I was trying to delete the post so people didn't feel like they needed to keep answering it. I was able to work out the answer on my own earlier. Thanks for the help though. I think we are on the same page.

I'm going through a abstract algebra book I found and am trying to learn more about group theory by going through some of the proofs and practice sets, but am having trouble with the following: Prove that G={a+b*sqrt(2) | a,b E R; a,b not both 0} is a group under ordinary multiplication...

I'm going through a abstract algebra book I found and am trying to learn more about group theory by going through some of the proofs and practice sets, but am having trouble with the following: Prove that G={a+b*sqrt(2) | a,b E R; a,b not both 0} is a group under ordinary multiplication...

DeMoivre' Thm

I think I got it

I think I got it