Intereting Posts

Is the Law of Large Numbers empirically proven?
Motivation behind standard deviation?
Wave equation with initial and boundary conditions – is this function right?
Simple Logical reasoning question
A certain inverse limit
What nice properties does exponentiation have?
Do we have always $f(A \cap B) = f(A) \cap f(B)$?
Sum of Cauchy Sequences Cauchy?
Fourier series for $f(x)=(\pi -x)/2$
Density of first hitting time of Brownian motion with drift
Image of ring homomorphism $\phi : \mathbb{Z} \to \mathbb{Q}$?
$\pi_{1}({\mathbb R}^{2} – {\mathbb Q}^{2})$ is uncountable
Is metric (Cauchy) completeness “outside the realm” of first order logic?
Beta function derivation
Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$

Let $N$ be a normal subgroup of $G$ such that every subgroup of $N$ is normal in $G$ and $C_G(N)\subseteq N $ .Prove that $G/N$ is abelian.

I think we need to use that every subgroup of $N$ is normal in $G$ but i can’t use .Please help me with Hints.

- Does $A\oplus \mathbb{Z}\cong B\oplus \mathbb{Z}$ imply $A\cong B$?
- Showing that a cyclic automorphism group makes a finite group abelian
- number of subgroups index p equals number of subgroups order p
- Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
- Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups?
- Sum of elements of a finite field

- An element of $f$ of a function field such that $P$ is the only pole of $f$.
- Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.
- Rings and modules of finite order
- Generating connected module over a connected $K$-algebra
- Ring with finitely many zerodivisors
- Field of sets versus a field as an algebraic structure
- Why are modular lattices important?
- What is a good book for a second “course” in group theory?
- What are the differences between rings, groups, and fields?
- Commutative integral domain with d.c.c. is a field

Let $a \in N$, $b,c \in G$. Since $\langle a \rangle$ is normal in $G$, it is normalized by $b$ and $c$.

The automorphism group of a cyclic group is abelian, so $b^{-1}c^{-1}bc$ centralizes $\langle a \rangle$. Now this is true for all $a \in N$, so $b^{-1}c^{-1}bc \in C_G(N) \le N$.

- Derivative of $x^x$
- Solving the recurrence relation $T(n)=2T(n/4)+\sqrt{n}$
- A sequence with infinitely many radicals: $a_{n}=\sqrt{1+\sqrt{a+\sqrt{a^2+\cdots+\sqrt{a^n}}}}$
- weak sequential continuity of linear operators
- $f,g$ continuous from $X$ to $Y$. if they are agree on a dense set $A$ of $X$ then they agree on $X$
- Intuitive reason why sampling without replacement doesnt change expectation?
- Proof $ \int_0^\infty \frac{\cos(2\pi x^2)}{\cosh^2(\pi x)}dx=\frac 14$?
- Entire function bounded by polynomial of degree 3/2 must be linear.
- what does ∇ (upside down triangle) symbol mean in this problem
- Are there any ways to evaluate $\int^\infty_0\frac{\sin x}{x}dx$ without using double integral?
- Find $\lim_{n \to \infty} \left$ (a question asked at trivia)
- Evaluate: $\int_0^2 (\tan^{-1} (\pi x) -\ tan^{-1} x) \ \mathrm{d}x$
- The Degree of Zero Polynomial.
- Show that $\int_{-\pi}^\pi ~f(x) \cos (nx) \mathrm{d}\mu(x)$ converges to $0$
- Differential Geometry without General Topology