query: Prove the $z=[x,y]$ is nilpotent.
positive_passages.docid: 156443
positive_passages.text: if $x$ and $y$ commute with $[x y]$, then $[x y]$ is nilpotent
negative_passages.docid: 102175
negative_passages.text: $Z=XY$, $E_Z[Z]$, $E_{X,Y}[XY]$
negative_passages.docid: 133019
negative_passages.text: Nilpotent elements in $\mathbb Z_n$
negative_passages.docid: 23517
negative_passages.text: Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
negative_passages.docid: 85525
negative_passages.text: Prove that $x^3+x+1$ splits in $Z_2[x]/(x^3+x+1)$
negative_passages.docid: 63882
negative_passages.text: Show that the heisenberg group is nilpotent
negative_passages.docid: 142530
negative_passages.text: Let K be a field, and $I=(XY,(X-Y)Z)⊆K[X,Y,Z]$. Prove that $√I=(XY,XZ,YZ)$.
negative_passages.docid: 54479
negative_passages.text: If $x,y$ are nilpotent and commute, $x+y $ is nilpotent.
negative_passages.docid: 121100
negative_passages.text: Rootspaces are $\mathop{ad}$ nilpotent
negative_passages.docid: 3820
negative_passages.text: Prove that $||x|-|y||\le |x-y|$
negative_passages.docid: 104855
negative_passages.text: Prove that $N \subset Z(G)$
negative_passages.docid: 17510
negative_passages.text: Proving a set is an abelian group.
negative_passages.docid: 13346
negative_passages.text: If $A=AB-BA$, is $A$ nilpotent?
negative_passages.docid: 112701
negative_passages.text: Prove that if matrix $A$ is nilpotent, then $I+A$ is invertible.
negative_passages.docid: 150738
negative_passages.text: Proof of $(A - B) - C = A - (B \cup C)$
negative_passages.docid: 34693
negative_passages.text: Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
negative_passages.docid: 74318
negative_passages.text: Find the nilpotents in $\mathbb{Z}_3[x]/(x^2-1)$