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5h
comment subgroup having index $2$ of $R^*$
But this "set of all squares" is a specific subset, with a much nicer description...
5h
answered subgroup having index $2$ of $R^*$
5h
comment If $a$ is the only element of order $2$ in a group, show that $a$ is in the center of the group.
If $|G|=2$, you're done. Otherwise, suppose $x$ is your element of order two. Then there exists some $g\in G\setminus\{1\}$ such that $x\neq g$. Consider $gxg^{-1}$ (the "conjugate" of $x$ by $g$).
Jan
12
comment Should BODMAS not be BODMSA?
@egreg That is basically what I tell my students: subtraction doesn't exist - it is just a figment of their school teachers imagination! (For division, I find it interesting that a/b/c looks "odder" to my eyes than a-b-c, and I wonder if this is true of everyone. But yes, it is exactly the same issue.)
Jan
12
comment Example of subgroup $H$ with the property $g H g^{-1}$ is properly contained in $H$.
Links die, so it is useful to accompany a link with something about what it contains - for example, here just give the example without proof!
Jan
6
awarded  Popular Question
Nov
14
revised Tarski Monster group with prime $3$ or $5$
N_i is abelian
Oct
21
comment Make set of ismorphisms between two groups into a group?
By $fg(x)$ I mean $f(g(x))$ (while some people - me included usually! - mean $g(f(x))$), so $(f\star \phi f^{-1})(x)=f(\phi^{-1}(\phi f^{-1}(x)))=x$ for all $x$.
Oct
21
answered Make set of ismorphisms between two groups into a group?
Oct
13
comment Name for a set of coset representatives which contains a transversal
When I said "quotient group" in the first line, I was implicitly assuming $N$ was normal in $G$ (else it wouldn't be a quotient group).
Oct
13
reviewed Edit Diophantine equations - how to go about it?
Oct
13
revised Diophantine equations - how to go about it?
deleted 24 characters in body
Oct
13
reviewed Close An inequality with real index
Oct
13
reviewed Leave Open When is differentiating an equation valid?
Oct
13
asked Name for a set of coset representatives which contains a transversal
Sep
29
comment Open mathematical questions for which we really, really have no idea what the answer is
I have had a quick search for the paper of Ol'shanskii and Sapir, and it seems that they haven't written a paper together since 2006 source. So...I am not precisely sure what I was thinking. Sorry.
Sep
29
comment Open mathematical questions for which we really, really have no idea what the answer is
@PaulPlummer If I remember correctly, my point was based on the sentence "Apparently, Rips gave a possible method of constructing such a group, but Ol'shanskii and Sapir turned his handle to no avail" and the associated link. The link reaffirms your impression that "most think there should be such a group", and gives a "general idea" for constructing such a group. However, from memory, between that post (2011) and my post (2014) Ol'shanskii and Sapir made this idea "work" but, as the sentence points out, it wasn't good enough. However, my dates may be incorrect (I haven't linked to the paper).
Jun
30
comment Integral involving a trig. term
Doesn't the fact that you've written the $dx$ to the left of the function you are trying to integrate matter? (I understand what you're saying, and my comment is entirely tangential: I just feel that what you've written doesn't actually makes sense, but would be interested if my intuition was wrong...)
Jun
25
comment How to integrate $\int^{\infty}_{-\infty} e^{-2\pi^2/x^2} dx$?
You need brackets. Do you mean $\displaystyle\frac{e^{-2\pi}}{x^2}$? Or $\displaystyle\frac{e^{-2}\pi}{x^2}$ Or $\displaystyle\left(\frac{e^{-2\pi}}{x}\right)^2$? Or something else?
Jun
25
asked $e^{i\theta}$ versus $\cos\theta+i\sin\theta$