Intereting Posts

Inequalities from Taylor expansions of $\log$ functions
Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx $ using contour integration
Find the limit of $(e^{2x}+1)^{1/x}$
Do we know if there exist true mathematical statements that can not be proven?
Derivative at x=0 of piecewise funtion
Explicit well-ordering of $\mathbb Q$
Alternative method of solving $\int_0^{\pi/2} {\sin^2{x} \ln{\tan x} \,dx}$
Is the complement of the closed unit disk in the plane homeomorphic with $\mathbb R^2\setminus \{(0,0)\} $ ?
Simple question: the double supremum
How to prove that the spectral radius of a linear operator is the infimum over all subordinate norms of the corresponding norm of the operator.
Can a finitely generated group have infinitely many torsion elements?
How to prove $P(A) \cup P(B) \subseteq P(A \cup B) $
Determinant of a special $n\times n$ matrix
Simple proof for finite groups that $g^{\#(G)}=1$
Maximum integer not in $\{ ax+by : \gcd(a,b) = 1 \land a,b \ge 0 \}$

Let $N= GL_n(\mathbb{R})$ and $M=SL_n(\mathbb{R})$. Is $M$ normal subgroup in $N$? Why or why not?

I know how to do this with $GL_2(\mathbb{R})$ and $SL_2(\mathbb{R})$ but with $N= GL_n(\mathbb{R})$ and $M=SL_n(\mathbb{R})$ I don’t even know all of their elements so I can’t check the left and right cosets of $M$ in $N$.

- Why is $(3,x^3-x^2+2x-1)$ not principal in $\mathbb{Z}$?
- Definition of a nilpotent group.
- Abelianization of free product is the direct sum of abelianizations
- Generalisation of euclidean domains
- Describing the ideals for which $\operatorname{dim}_F(F/I) = 4$
- Why should I consider the components $j^2$ and $k^2$ to be $=-1$ in the search for quaternions?

- Is an automorphism of the field of real numbers the identity map?
- If the subgroup $H$ of $G$ is open in pro-$p$ topology, does it inherit the pro-$p$ topology?
- Finding inverse in non-commutative ring
- Why $a+b$ is a generator of $F(a,b)$ over $F$, where $F$ is a field of characteristic zero.
- What are the units of cyclotomic integers?
- Prime ideal and nilpotent elements
- $\frac{SU(2)}{N}= U(1) \times Z_2$. Find $N$?
- What's the rationale for requiring that a field be a $\boldsymbol{non}$-$\boldsymbol{trivial}$ ring?
- Does $\text{End}_R(I)=R$ always hold when $R$ is an integrally closed domain?
- What is a short exact sequence telling me?

Remember that $H$ is normal in $G$ if $ghg^{-1} \in H$ for all $g \in G$, $h \in H$. Also note that for square matrices $A, B$ we have $\det(AB) = \det(A)\det(B)$.

Hint:

Is the determinant map

$$\det:GL_n(\Bbb R)\to\Bbb R^*\,$$

a homomorphism….?

- Connection between the area of a n-sphere and the Riemann zeta function?
- Convergence of a series $\sum\limits_{n=1}^\infty\left(\frac{a_n}{n^p}\right)^\frac{1}{2}$
- Can monsters of real analysis be tamed in this way?
- Is this AM/GM refinement correct or not?
- Is there a garden of derivatives?
- Why is $n$ divided by $n$ equal to $1$?
- Is the set of all $n\times n$ matrices, such that for a fixed matrix B AB=BA, a subspace of the vector space of all $n\times n$ matrices?
- Weak Hausdorff space not KC
- $R>r>0$ , $||a||,||b||<r$ ; is there a diffeomorphism on $\mathbb R^n$ switching $a,b$ ;identity for $||x||>R$ ; pulls back volume form to itself?
- Decomposition of a prime number $p \neq l$ in the quadratic subfield of a cyclotomic number field of an odd prime order $l$
- How to find the values that make this interval enclose an integer
- Evaluation of $\int\frac{(1+x^2)(2+x^2)}{(x\cos x+\sin x)^4}dx$
- Integral of odd function doesn't converge?
- How to obtain a Lie group from a Lie algebra
- A variant of Kac's theorem for conditional expectations?