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I'm a student of mathematics in Germany.


May
3
comment Rays in the space
Assuming $n$ is a positive integer, the smallest such $n$ is $n$ itself. But only if it has the above-mentioned property to begin with!
May
3
answered If $g$ is discontinuous and $fg$ is continuous then $f$ is continuous
May
3
comment If $g$ is discontinuous and $fg$ is continuous then $f$ is continuous
@TZakrevskiy The questions reads “such that for all discontinuous functions $g$ …”.
May
2
comment Let $H,K \trianglelefteq G$. Show that if $H$ and $K$ are solvable then the subgroup $HK$ is solvable.
Sorry, I actually didn’t think this through, I was thinking of quotients that aren’t there. So probably $HK_0 \trianglelefteq HK_1 \trianglelefteq … \trianglelefteq HK_m = HK$ is indeed a normal subseries with abelian quotients since $HK_i/HK_{i-1} \cong K_i/(HK_{i-1}∩K_i)$ by the second isomorphism theorem, and $K_{i-1} \trianglelefteq HK_{i-1}∩K_i$, so $K_i/(HK_{i-1}∩K_i) \cong \tfrac{K_i/K_{i-1}}{HK_{i-1}∩K_i/K_{i-1}}$ by the third isomorphism theorem, a factor of an abelian group. But that isn’t the simplest way, Pedros way is much prettier.
May
2
comment Let $H,K \trianglelefteq G$. Show that if $H$ and $K$ are solvable then the subgroup $HK$ is solvable.
You didn’t use that $K$ is solvable so far. Maybe you want to employ that and refine the step $H \trianglelefteq HK$ a bit by using the correspondence theorem on the subnormal series $\{e\} = K_0 \trianglelefteq K_1 \trianglelefteq … \trianglelefteq K_m = K$.
May
2
revised Equivalent characterizations of group objects
added 1 character in body
May
1
comment Equivalent characterizations of group objects
@MarianoSuárez-Alvarez Okay, suit yourself. I hope I wasn’t too rude, but for the record: I was actually a bit offended by your comments, so that’s why.
May
1
comment Equivalent characterizations of group objects
@MarianoSuárez-Alvarez Also, “our exercise” and “our lecture” should also give away enough context to at least not assume the less likely possibility of a textbook problem I’m trying to solve myself, which I wouldn’t regard as homework and for which I don’t think the homework tag is suitable at all.
May
1
comment Equivalent characterizations of group objects
@MarianoSuárez-Alvarez No, which one is incompatible with good academic practices?
May
1
answered Equivalent characterizations of group objects
May
1
comment Equivalent characterizations of group objects
@MarianoSuárez-Alvarez Yeah, this should have been absolutely clear considering the statements “Now, our exercise is to show …”, “Any hints are greatly appreciated.” and the homework-tag.
May
1
comment Equivalent characterizations of group objects
@MarianoSuárez-Alvarez That’s not the point. Homework questions are ideally answered individually, responding to the points where people get struck. Of course, I can address these points pretty well myself now, but nevertheless – it feels a bit pointless to give an individual answer or “hints” to myself. The alternative would be to give a full answer, as it is suggested for answering one’s own question, but this (at least generally) would mean giving away a solution to a pending assignment which I think should be discouraged as well. On the other hand, … who cares?
May
1
revised Equivalent characterizations of group objects
added 1 character in body
May
1
comment Equivalent characterizations of group objects
@Hurkyl It may be that others visiting this site still need to do the exercise. On the other hand, … 11 views.
May
1
revised Equivalent characterizations of group objects
added 128 characters in body
May
1
revised Equivalent characterizations of group objects
added 98 characters in body
May
1
asked Equivalent characterizations of group objects
Apr
30
answered Suppose $z \neq -1$ is a complex number of norm 1. Prove that $(\frac{1+z}{|1+z|})^2 =z $
Apr
30
awarded  Cleanup
Apr
29
comment Exponents in Identities
I’ve edited the formula – is that what you meant?