Verifying that the symmetric group $\mathsf{S}_m$ acts on $\mathbb{N}^m$
111348
Show that $\mathrm{S}_{m} \times \mathbb{N}^{m} \rightarrow \mathbb{N}^{m}$ defines an action of $\mathrm{S}_{m}$ on $\mathbb{N}^{m}$
79055
Orders of a symmetric group
158127
Quotient space of $\Bbb C^n$ obtained by action of $S_n$
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
120035
Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$
68211
Characters of Symmetric and Antisymmetric Powers
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
8456
Prove that $SL(2,\mathbb{R})$ acts transitively on the upper half plane
7324
Let $H$ be a subgroup of $G$ with $[G:H]=n$. Let $N$ be the kernel of the left-multiplication action on the cosets of $H$. Show $[G:N]$ divides $n!$
92211
When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
41294
Permutation module of $S_n$
115182
Centre of symmetric group algebra
145220
Homology Groups of $S^n$
87922
Computing the Lie bracket on the Lie group $GL(n, \mathbb{R})$
157806
Order of a element on a Symmetric Group
110325
proof of basic fact that torus actions are diagonalizable
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime