Intereting Posts

How to prove that $1+2=3, 4+5+6=7+8,… $ ad infinitum?
The constant of integration during integration by parts
Finding the coordinates of points from distance matrix
On the trigonometric roots of a cubic
Example of a boundary point that is not simple
if eigenvalues are positive, is the matrix positive definite?
Alice and Bob are flipping coins…
Can every closed subspace be realized as kernel of a bounded linear operator from a Banach space to itself?
Prove the integral property of $B \cap B$, where $y=x^{-1}$
Can the Negation of a Conditional Implying the First Atomic Proposition Get Proven in Around 50 Steps?
How to prove that the Fibonacci sequence is periodic mod 5 without using induction?
Prove that if $p$,$q$ and $\sqrt{2}p+\sqrt{3}q$ are rational numbers then $p=q=0$
Projective Noether normalization?
Coordinates of the intersection points between an ellipse and a chord line
On the structure of $\operatorname{Aut}(\Im z>0)$

For $a=\cos(2\pi/n)$, show that $[\mathbb{Q}(a):\mathbb{Q}] = \{1 \text{ for } n=1,2; (1/2)\phi(n) \text{ for } n>2\}$.

$\phi$ is the Euler totient function which gives the number of coprime elements.

We are new to abstract algebra. This is a question on a difficult project involving cyclotomic polynomials and their irreducibility.

- Examples of finite nonabelian groups.
- Generating the symmetric group $S_n$
- Question about notation for Minors / How to determine a set of invariant factors given a relations matrix
- Length of the tensor product of two modules
- Let Q8 represent the group of quaternions and V4∼= Z/2Z ⊕ Z/2Z represent the Klein four-group.
- Distinguishable painted prisms with six colors (repetition allowed)

We know that the degree of the cyclotomic extension is just $\phi(n)$, but obviously $a$ is just one piece of the roots of unity.

- How to prove the group of automorphisms of $S^1$ as a topological group is $\mathbb Z_2$?
- Compute this factor group: $\mathbb Z_4\times\mathbb Z_6/\langle (0,2) \rangle$
- $H^1$ of $\Bbb Z$ as a trivial $G$-module is the abelianization of $G$
- Good abstract algebra books for self study
- Give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain
- Extending Herstein's Challenging Exercise to Modules
- Factoring $X^{16}+X$ over $\mathbb{F}_2$
- In which of the finite groups, the inverse of Lagrange's Theorem is not correct?
- Minimal Polynomial of $\zeta+\zeta^{-1}$
- $M \oplus M \simeq N \oplus N$ then $M \simeq N.$

- Expected max load with $n$ balls in $n$ bins?
- Is there an absolute notion of the infinite?
- if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
- Simultaneous Maximization and Minimization
- Chinese Remainder theorem with non-pairwise coprime moduli
- Need a counter example for cycle in a graph
- Neumann series and spectral radius
- Proof by induction of Bernoulli's inequality: $(1 + x)^n \geq 1 + nx$
- Showing Equality of Winding Numbers
- Prove the Radical of an Ideal is an Ideal
- What exactly *is* the Riemann zeta function?
- Why is two the only even number that is prime?
- Why can't erf be expressed in terms of elementary functions?
- Show that the square of any prime number is the Factof of some integer
- Why $PSL_3(\mathbb F_2)\cong PSL_2(\mathbb F_7)$?