query: Is the following proof of $Z(S_n)=\{id\}$ correct?
positive_passages.docid: 11627
positive_passages.text: Find the center of the symmetry group $S_n$.
negative_passages.docid: 37928
negative_passages.text: Isomorphism between $D_{2n}/Z(D_{2n})$ and $D_n$
negative_passages.docid: 75317
negative_passages.text: Show that $(s_n)$ is a Cauchy sequence
negative_passages.docid: 92583
negative_passages.text: Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
negative_passages.docid: 14759
negative_passages.text: Prove that $ f(z) = 0 $ for all $ z \in \overline{D}(0,1) $.
negative_passages.docid: 26302
negative_passages.text: Prove that $(X \cap Y) \cup Z = (X \cup Z) \cap (Y \cup Z)$
negative_passages.docid: 4648
negative_passages.text: Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 79056
negative_passages.text: Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
negative_passages.docid: 67926
negative_passages.text: $S_n$ is generated by elements of the form $(1k)$
negative_passages.docid: 1125
negative_passages.text: Inductive proof that ${2n\choose n}=\sum{n\choose i}^2.$
negative_passages.docid: 136855
negative_passages.text: Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID
negative_passages.docid: 44802
negative_passages.text: The $n$ complex $n$th roots of a complex number $z$
negative_passages.docid: 106767
negative_passages.text: $|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
negative_passages.docid: 100968
negative_passages.text: Why is $|e^{i \lambda z}| |e^{- \lambda y}|= |e^{- \lambda y}|$ here?
negative_passages.docid: 16172
negative_passages.text: My proof of $I \otimes N \cong IN$ is clearly wrong, but where have I gone wrong?
negative_passages.docid: 31451
negative_passages.text: Proving a subring of $\mathbb{Q}$ containing $\mathbb{Z}$ is a PID