I'm a first-year, so just learning about things involved in what I might work in; it looks like that might be low-dimensional topology. I'm trying to learn some of the basic Floer homology theoey and am taking a gauge theory course in the winter.
@Venus I'd be very tough (totally correct I mean) as a ruler, and probably I got annoyed many many times that will lower terribly the quality of my life. Well, I appreciate your intention. You also have my vote! :-)
Oh, this is awesome. By sylow theorems, it has precisely 1 sylow-subgroup of order 13, and one of order 31. If it would've had precisely 1 of order 5, than it would be the product of these cyclic-subgroups, which would mean it is abelian - contradicting the fact it's non abelian.
@Alizter The product of any two countable infinite groups is countablt infinite; the product of an infinite group with a finite group is infinite; the countable direct sum of (at most countable) groups is infinite
@Mike no need for nilpotent - the theorem states that if $G$ is of finite order $n$, $n=p_1^{k_1}*p_2^{k_2}*...$, and for every $p_i$, $G$ has a singly sylow-subgroup of order $p_i$, then $G$ is the cross-product of all it's sylow subgroups
@Alizter I think you need to make it more precise to make anything of it. What does it mean to have negative order? What does it mean to be "something like a group"?
$$F(\theta)=\sin(\theta)\int_{-l}^{l} e^{-ikz\cos \theta} h(z)\,dz$$
We know that $F(\theta)$ is defined on $0\le \theta \le \pi$ and $h(z)$ is defined on $|z|\le l$ and $z$ is real in this case, but it might be complex too!
That is all we know, how can we find the $h(z)$ by having knowledge of $...
Do there happen to be any known results about the spectrum of $S_l + S_r$, where $S_l$ and $S_r$ are the left and right shifts on $l_2[0,\infty)$? If I knew that I could solve a problem I've been working on unsuccessfully for what feels like ages.
@Alizter I mean, you first need to write down a theory and notion of cardinality in which such things exist. Asaf's answer is that for negative cardinality, any such theory has bad qualities. It's not obvious how to get any naively from the notion of rational cardinality. But I bet if you wrote down such a thwory I would call it silly.
@FreeMind You post what appears to be a pretty difficult question with no background. Here it would probably be closed as not having enough background or because you have not shown work. On MO, it just sits.
@robjohn Because I have no idea to beat it, the question is what it is, and it is supposed to be solved with that limited background, if it was easy, I would not ask it on MO and I would solve it sooner.The problem is, it gives the same feeling to me as the one who intends to help me to solve it.
@FreeMind When you ask about it, I try to work on it and then you disappeared from chat before I came back. I computed the FT but the kernel you get does not seem to offer an easy way to invert to get $h$ from $F$
@FreeMind I thought you said you had a way to solve it, but you were looking for another way.
@robjohn I have a way not completely from me, but from a book, and that book offers a complex analysis approach, but the person who asked me this question, told me, it should be solved and approximated(not exactly) by the fourier series basic methods
@robjohn And you are right, I left the chat and it was my fault, because I was so frustrated, every time I see this integral, I feel like shit.
@robjohn Even the approach in the book is hard to follow.
@robjohn Can you make a chat room so I can share the link of the book?
