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 Apr21 comment $[U \cap H : G \cap H] \le [U :G]$ @ClémentGuérin An unfortunate choice of notation by the OP ($U$ being the ambient group). Anyway, my suggestion for the set of left cosets of $U$ modulo $G$ is...ta-daa! $(U/G)_L$ ($L$ stands for "left"). Apr16 reviewed Approve Positive solutions of $893x - 2432y = 19$ Apr10 comment Let $A,B$ be two $3\times 3$ matrices with complex entries, such that $BA^2=A^2B$. Prove that $\det(AB-BA)=0$ I have one question: why $3\det(AB-BA)=\mathrm{trace}\bigl[(AB-BA)^3\bigr]$? Apr10 comment Let $A,B$ be two $3\times 3$ matrices with complex entries, such that $BA^2=A^2B$. Prove that $\det(AB-BA)=0$ My friend, it seems that you are well aware of the property $\mathrm{trace}(WZ)=\mathrm{trace}(ZW)$. Use this property one more time on your last line!!! (take $W=A, Z=BABAB$). Apr3 reviewed Approve A question regarding rational functions being onto. Apr3 comment Is there a closed-form of $\sum_{n=1}^{\infty} \frac{\sin(n)}{n^4}$ I would try to work with the imaginary part of the series $\sum_{n=1}^\infty\frac{e^{inx}}{n^4}$, and afterwards to evaluate at $x=1$...I am lazy now, sorry. Mar28 reviewed Approve Why are two permutations conjugate iff they have the same cycle structure? Mar28 reviewed Reject Matrix can be orthogonally diagonalized iff its eigenvectors are linearly independent Mar23 awarded Revival Mar22 answered Is the following set connected given that the union and intersection is connected Mar19 comment Find a subring $D$ of ring $D'$ such that: $D'$ is a UFD but not a field, and $D$ is an ID but not a UFD. ID=Integral Domain? Mar13 revised When, how & who first gave this calculation of $\pi$ added 5 characters in body Mar12 comment A Dedekind Finite Non-Regular Ring What is the definition of "Dedekind finite ring"? Mar2 revised Multi-index power series added 7 characters in body; edited title Feb17 reviewed Edit Order of an entire function represented as an infinite product Feb17 revised Order of an entire function represented as an infinite product Formatting math; tag Feb16 comment Does a non-trivial solution exist for $f'(x)=f(f(x))$? @Julien I strongly suggest you to explicitly describe the domain of the function on the statement of the problem, something like "Is there some function $f:\mathbb R\to\mathbb R$ other than $0$ satisfying $f'=f\circ f$?" Jan24 comment uniform continuity and equivalent sequences Your definition of equivalent sequences $(a_n)_{n\geq1}$ and $(b_n)_{n\geq1}$ simply says that the difference $a_n-b_n$ tends to $0$ (no matter whether or not each single sequence converges). Jan11 answered If $f(x)$ be a polynomial function satisfying $f(x).f(\frac{1}{x})=f(x) +f(\frac{1}{x})$ and $f(4) =65$ then find $f(6)$ Jan9 comment Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$ Problem 11651 of the American Mathematical Monthly is closely related to your problem (see the solution here). Also, see this paper.