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Jan
11
comment Question in Complex Analysis
@MichaelAlbanese I doubt whether OP really understands differential forms.
Jan
11
revised Flood algorithm - find polygon containing a given point.
edited tags
Jan
11
comment Could a group embed normally in another group in which any automorphism is attained by conjugation?
I considered the embedding from $G$ into $\operatorname{Sym} G$. It's not normal, though. However, I didn't realize that the normalizer simply works.
Jan
11
comment Could a group embed normally in another group in which any automorphism is attained by conjugation?
Is there any intuition on semi-direct products? I met it in many situations, but all of them are algebraic constructions. I didn't see any other perspective, for example, from group action, or the viewpoint of transformation group.
Jan
11
accepted Could a group embed normally in another group in which any automorphism is attained by conjugation?
Jan
11
comment Could a group embed normally in another group in which any automorphism is attained by conjugation?
@DerekHolt Sounds good. Could you please write a complete answer? (I'm not familiar with these concepts, but after a glance at wikipedia, it seems right.)
Jan
11
asked Could a group embed normally in another group in which any automorphism is attained by conjugation?
Jan
3
awarded  Informed
Jan
3
comment Is it possible to prove that $K\subseteq C(G)$
$kgk^{-1}g^{-1}=k(gk^{-1}g^{-1})\in K$
Jan
3
accepted Should diffeomorphisms preserving arc length be affine?
Jan
3
comment Should diffeomorphisms preserving arc length be affine?
Could you assimilate these comments into the answer? And even better, could you point out some elementary reference that the isometry of a pseudo-Riemannian manifold is locally determined?
Jan
2
comment Should diffeomorphisms preserving arc length be affine?
And why is an isometry determined by the first order data at a point? It looks like a localization.
Jan
2
comment Should diffeomorphisms preserving arc length be affine?
Tomorrow I'll check it in details. At a first glance, it seems that the proof relies on a smooth condition of $\varphi$, i.e. $\varphi\in C^2$. I don't know whether it's still true for $\varphi\in C^1$. However, that's not important to me (I don't care the smoothness condition).
Jan
1
comment How to calculate the inverse of a complex matrix?
In fact, it works for any arbitrary field $K$ instead of $\mathbb C$, or unitary commutative rings in which $ad-bc$ is invertible.
Jan
1
comment Show $S_4$ is not isomorphic to $D_{24}$ by looking at their centers
Proof for the triviality of the center of $S_4$: the conjugate $gag^{-1}$ of $a$ is just a relabeling of $a$. For example, if $a=(123)$, then $gag^{-1}=(g(1)g(2)g(3))$. It's not hard to show that if $a\neq 1$, the identity, then the conjugate class of $a$ isn't a singleton.
Dec
30
asked Does the implicit function theorem imply Peano existence theorem
Dec
29
comment Question about integral on hypersurface
Note that the ordinary surface integral gives a positive linear functional on $C_c(S)$, the space of continuous compactly supported functions on $S$, where $S\subseteq\mathbb R^n$ is locally compact Hausdorff. The Riesz representation theorem furnishes a Riesz measure on the surface $S$.
Dec
29
awarded  Custodian
Dec
29
revised Solving recurrences with summation factors (Concrete Mathematics)
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Dec
29
revised Should diffeomorphisms preserving arc length be affine?
edited title