Thank you very much for your reply! I did indeed use ϴ to denote the zero element (sorry!)
Just to clarify, I could've just as well considered (1+√-17)?:)
And I really do apologise for my ignorance, but I don't see why for example we have the relation (p_3)^2~(q_3)^(-2)~p_2 and not just...
I have a pretty urgent question concerning the calculation of the class group, so any help will be very much appreciated:)
I'd like to illustrate my question with an example:
Calculate the ideal class group of Q(√-17), giving a representative ideal for each ideal class and a description of the...
hmm, I did consider (x+1)^43 + 43(x+1) + 85 at one point, but my lack of intuition makes it hard for me to understand why we make the substitution, since, if I'm not mistaken; if we take the prime p=43, immediately we can see E's criterion is satisfied.
Ah, I think I just had a light bulb...
Hello,
I have a couple questions concerning Eisenstein's Criterion;
1) by making a substitution of the form x |-> x + a, show x^43 + 43x + 85 is irreducible over Q.
2) completely factorize into monic irreducible factors over Q for x^36 + 36x^8 - 405.I've only come across other examples to...
ah, fantastic!:) Thanks a lot!
...so there are 8(7-1) = 48 elements of order 7, leaving 8 elements after 56 - 48.
And since we know there is a subgroup of order 8, we can now deduce that this is indeed unique.
Hence it follows; subgroup of order 8 is a normal subgroup in G.
Got it - thanks...
Hello,
I'm having difficulty understanding how to solve the following question using Sylow's Theorem:
Suppose G is a group of order 56. Show that either:
i) G has a normal subgroup of order 7 or
ii) G has a normal subgroup of order 8.
I started by decomposing 56 into desired form...
Wisvuze, thanks!
After reading your comment I attempted the question again and saw my mistakes immediately. I can only blame it on the fact that it was past 1 in the morning:) I'm aware of Sylvester's Law of Inertia - however, I couldn't get the fact it had a unique rank/signature since I kept...
could someone please explain briefly what the problem is with my method of finding such canonical forms.
The method we've been taught is to find the canonical form by performing double row/column operations on the matrix representation of quadratic form until we get to a diagonal matrix, and...