Homework Statement
Let G be a group acting transitively on a set S. for a and b elements in S which are distinct, show that the product of the stabilizer of a and the stabilizer of b is not equal to G.
Homework Equations
The Attempt at a Solution
I was trying to use the...
Homework Statement
Construct a finite field of order 16. And find a primative element.
Homework Equations
The Attempt at a Solution
What I did was find an irreducible polynomial in Z/<2> of degree 4. I used f(x)=x^4+x+1.
Then I took a to be a root of f(x) and set a^4=a+1...
Ok, I think it all comes together now. The only part I want to be sure of is, given a sequence {(x,y)n} in AxB which converges to (x,y), then is it as obvious as it seems that xn converges to x in A and yn converges to y in B? Does this require a proof?
If not than I think I can now show...
I believe that if y is fixed then dy(x) = d(x,y) is continuous by a very simple epsilon delta proof. Is this what you mean? If so d(xn,y) converges to d(x,y). Does this automatically give us that d(xn,yn) converges to d(x,y)?
Homework Statement
For a metric space (M,d) and two compact subspaces A and B define the distance d(A,B) between these sets as inf{d(x,y): x in A and y in B}. Prove that there exists an x in A and a y in B such that d(x,y)=d(A,B).
Homework Equations
The Attempt at a Solution
I...
Homework Statement
Given a commutative ring with unity, show that if every ideal is prime than the ring is a field.
Homework Equations
The Attempt at a Solution
I think that I can show that a ring is a field iff it has no nontrivial ideals. So I guess I need to show that if a...
Homework Statement
Show that a group of order 12p is solvable for any prime p greater than 11
Homework Equations
I'm not very good about solvability questions so if anybody has any good ideas I'd be interested to hear them.
The Attempt at a Solution
I know that that every group...