Yeah, I see that now...
Well, its obvious that <a> is contained in <b>
Not sure how I can use the fact that a and b have the same order to prove the other direction, any hints?
Homework Statement
Suppose a \in <b>
Then <a> = <b> iff a and b have the same order (let the order be n - the group is assumed to be finite for the problem).
Proof:
Suppose a and b have the same order (going this direction I'm trying to show that <a> is contained in <b> and <b> is...
Close but you are missing one thing.
Maybe if you saw another example it would become more clear...
What is the derivative of sin(2x)?
Or if you prefer by the definition of the chain rule:
(f \circ g)' = f'(g) * g'
In your case, what is f and what is g?
Then can you see your mistake?
Not correct:
First, what is the derivative of e^(2x) ?
Second, if f and g are arbitrary functions of x, what is the derivative of f*g with respect to x (ie, what does the product rule say)?
Homework Statement
Suppose G is a group, H < G (H is a subgroup of G), and a is in G.
Prove that a is in H iff <a> is a subset of H.
Homework Equations
<a> is the set generated by a (a,aa,aa^-1,etc)
The Attempt at a Solution
For some reason this seems too easy:
1. Suppose a...
Homework Statement
A is a subset of R and G is a set of permutations of A. Show that G is a subgroup of S_A (the group of all permutations of A). Write the table of G.
Onto the actual problem:
A is the set of all nonzero real numbers.
G={e,f,g,h}
where e is the identity element...
Homework Statement
G is an abelian group
Let H = {x \in G : x = x^{-1}
Prove H is a subgroup of G.
I have two methods in my arsenal to do this (and I am writing them out additively just for ease):
1. Let a,b be in H. If a + b is in H AND -a is in H then H<G.
or
2.Let a,b be in H...
So today in class we talked about defining equations...
We were asked to consider the group generated by <a,b>
with the defining equations a^2 = e, b^3 = e, and ba = ab^2. With these equations we can easily see that there can only be a maximum of 6 elements (and apparently most of the...
Homework Statement
If gcd(ab,c) = 1 then gcd(a,c)=1 and gcd(b,c)=1
2. The attempt at a solution
Well, if gcd(ab,c) = 1 we know that
abk + cl = 1 for some integers k and l
not really sure where to go from here... any hints?
Homework Statement
For some reason these are just messing me up. I need to prove:
1. \delta(y)=\delta(-y)
2.\delta^{'}(y) = -\delta^{'}(-y)
3.\delta(ay) = (1/a)\delta(y)
In 2, those are supposed to be first derivatives of the delta functions
Homework Equations
Use an integral...
Just started using wolframalpha.com for the integrals. Just wanted to make sure my syntax and what not was correct.
Have to draw it out to get the limits heh