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Dec
11
comment When does an element of $\mathrm{Sl}_n(\mathbb{R})$ preserve a scalar product?
Yes exactly. I'm not sure how to be clearer :)
Dec
11
revised When does an element of $\mathrm{Sl}_n(\mathbb{R})$ preserve a scalar product?
added 8 characters in body
Dec
11
comment When does an element of $\mathrm{Sl}_n(\mathbb{R})$ preserve a scalar product?
For example any conjugate of a rotation preserve a scalar product, but does not belong to $O_2(\mathbb{R})$.
Dec
11
comment When does an element of $\mathrm{Sl}_n(\mathbb{R})$ preserve a scalar product?
Not really. I'm looking for conjugates of the orthogonal group since the scalar product is not necesserally the canonical euclidean product in the canonical basis.
Dec
11
reviewed Approve When does an element of $\mathrm{Sl}_n(\mathbb{R})$ preserve a scalar product?
Dec
11
asked When does an element of $\mathrm{Sl}_n(\mathbb{R})$ preserve a scalar product?
Dec
4
comment Automorphism of the free group
I'm not sure I get what you want to say. If you read carefully Farb and Margalit(p.87, I guess there is only one edition), the mapping class group of the once punctured torus is isomorphic to the central extension of $GL(2,\mathbb{Z})$. Maybe you make the distinction whether the torus is thought with or without boundary. Nevertheless, I would be glad to have further explaination on this proof.
Dec
3
comment Automorphism of the free group
Could you detail a bit I'm not sure I understand your proof.
Dec
3
revised Automorphism of the free group
added 1 characters in body
Dec
3
revised Automorphism of the free group
added 142 characters in body
Dec
3
asked Automorphism of the free group
Nov
25
answered Let $x,y$ in a group G with odd order. Let $x^2=y^2$. Show that $x=y$.
Nov
25
accepted Defining a group morphism using generators
Nov
25
comment Defining a group morphism using generators
Yes I have edited. Then $\varphi)$ is trivial on $\mathcal{R}$. $\mathcal{R}$ is a word in $a$ and $b$. It is clear $\varphi$ must be trivial on $\mathcal{R}$. But does such a $\varphi$ exist ?
Nov
25
revised Defining a group morphism using generators
edited body
Nov
25
asked Defining a group morphism using generators
Nov
23
comment Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function.
Anyway your proof had to be false because you proved that $f'$ is continuous, what we clearly know to be false ! What would be great is to construct explicitly such function ... Is there here food for another $MSE$ question ?
Nov
23
comment Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function.
Sorry I may I have been a bit hard on your proof. There are 2 mistakes: 1) in the assumption that left and right limits exists of the derivative exists 2) the values of $d$ are not unspecified, they clearly depends on the values of $\frac{f(x) - f(c)}{x-c}$ so you cannot conclude $\lim_{c+} f' = A $. Is it clearer ?
Nov
23
comment Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function.
This proof is false. The relevant result is the Darboux theorem which is a bit deeper.
Nov
23
comment Calculate $ \int_{\partial D}\left ( 1+z+z^{2} \right ) (e^{\dfrac{1}{z}} +e^{\dfrac{1}{z-1}}+e^{\dfrac{1}{z-2}} ) dz$
Have you ever heard of the Residues theorem ?