Finding a bound for $[G:N]$
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 $n!$
127102
Upper bound for $\sqrt[n]{n!}$
26449
$|G|=24$ prove that $G$ is not simple
72843
Parity of number of factors up to a bound?
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
84132
Number of preimages of a group element under a homomorphism.
130751
Lower bound for monochromatic triangles in $K_n$
28658
$R$ with an upper bound for degrees of irreducibles in $R[x]$
140444
Prove $\chi(G)\chi(\bar{G}) \geq n$ for chromatic number of graph and its complement
144732
If $[G:H]=n$, then $g^{n!}\in H$ for all $g\in G$.
129845
Prove that $T$ is a subgraph of $G$
148470
bound of the function
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
148285
Generator of group $D_n$
104855
Prove that $N \subset Z(G)$
147596
Number of solutions to $x^n=e$ in group $G$ is divisible by $n$
57221
counting the number of elements in a conjugacy class of $S_n$