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olivier dot begassat dot cours at gmail dot com


Dec
11
comment 1-form on $S^n$ with non-degenerate differential.
@StevenGubkin I'm not sure that works, nothing keeps $w$ from vanishing. We only require $dw$ to never vanish.
Dec
11
comment finding all composition series of ${\rm sym} \ (4)$
In order to find all the maximal normal subgroups you should start off by listing all the normal subgroups : there aren't too many of them! Now just answer the question, which are maximal?
Dec
11
comment There is a surjective homomorphism from $\Bbb Z * \Bbb Z$ onto $C_2*C_3$
Well then you know what it is, it's the unique group up to isomorphism such that yada yada yada. From that definition alone you can at least work out that the canonical map $\Bbb Z\star\Bbb Z\to C_2\star C_3$ is an epimorphism without breaking a sweat, and epimorphisms are the same as surjective group homomorphisms. But the proof of that fact requires the tools you are currently learning I believe, so it's not entirely satisfying.
Dec
11
comment There is a surjective homomorphism from $\Bbb Z * \Bbb Z$ onto $C_2*C_3$
Has he defined the coproduct of groups in general at this point? Do you even know what $G\star H$ is for general groups?
Dec
11
revised Given a group homomorphism $R \otimes_{\Bbb{Z}} M \rightarrow M$, I need to show that this makes $M$ into a left $R$-module.
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Dec
11
comment show that the extension $\mathbb{Z}_{2}(X)\supseteq \mathbb{Z}_{2}(X^2+X)$ is Galois
I'm not an expert, but this seems perfectly fine to me.
Dec
11
comment Prove or disprove a function is continuous
For $V$, recall the standard basis for the product topology on $$\prod_{\Bbb R}\Bbb R$$, and intersect those sets with $C$.
Dec
11
comment Prove or disprove a function is continuous
Hi @henry, what do you want me to explain?
Dec
10
answered Given a group homomorphism $R \otimes_{\Bbb{Z}} M \rightarrow M$, I need to show that this makes $M$ into a left $R$-module.
Dec
10
comment The Tangent Disc Topology is developable
No, I must have clicked a second time, because there was no vote cast when I returned to see your comment. +1 Now
Dec
10
comment The Tangent Disc Topology is developable
I wouldn't expect an answer, people are downvoting left and right these days for no reason at all. +1
Dec
10
revised Prove or disprove a function is continuous
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Dec
10
revised Prove or disprove a function is continuous
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Dec
10
comment Latin phrase for “accepting without proof”
@DennisGulko look at the poster's reputation, it takes 50 reputation to post comments.
Dec
10
answered Prove or disprove a function is continuous
Dec
10
comment Numbers permutation
+1 nice answer, and I never knew of that result you link to.
Dec
9
comment Question about proof of subgroups
@YoavFridman Could edit your question to contain the exact statement that you are to prove? One possible correct statement would be $$\Big(\forall a\in G, aH=Ha\Big)\quad\Longleftrightarrow\quad\Big(\forall a\in G\forall h\in H, a^{-1}ha\in H\Big)\,.$$
Dec
9
comment Question about proof of subgroups
As it stands, the statement is incorrect, or at least very ambiguous. Are $a$ and $h$ fixed at the beginning, or are you trying to prove, given $a\in G$ that $$aH=Ha\quad\Longleftrightarrow\quad\Big(\forall h\in H,a^{-1}ha\in H\Big)$$?
Dec
8
comment How to prove or disprove that $\gcd(ab, c) = \gcd(a, b) \times \gcd(b, c)$?
Have you tried numerical examples? You should do so to either get a counter example, or on the contrary, convince yourself that the statement might be true.
Dec
8
comment What is the single most influential book every mathematician should read?
I liked the book (and thus upvoted). It's been years since I read it, but I remember working out some calculations with a recursive function $G$ that I thought were very cool back then.