Prove that $Z(S_n)$ is trivial for $n \geq 3$
11627
Find the center of the symmetry group $S_n$.
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
115782
Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz
150156
Proving that $S_n$ has order $n!$
44802
The $n$ complex $n$th roots of a complex number $z$
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
122330
Prove that there exists some $c\in(-3,3)$ such that$ \ \ g(c) \cdot g''(c)<0$.
36747
$\text{Tor}_0^R(M,N)\simeq M\otimes_R N$
23517
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
75317
Show that $(s_n)$ is a Cauchy sequence
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
44864
Prove, formally that: $\log_2 n! \ge n$ , for all integers $n>3$.
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$