Suppose n is even positive integer and $H$ is a subgroup of $\mathbb Z_n$
101345
Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is...
87766
Using Cayley's Theorem to find an isomorphic subgroup.
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
132342
Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?
133770
Subgroups of finite abelian groups.
4648
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 $d=\gcd(m,n)$
124709
Suppose G be a non-abelian group and H,K be two abelian subgroups of G. Then must HK be an abelian subgroup of G?
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
33387
Proof that $n\Bbb Z \leq \Bbb Z$ and are the only subgroups of $\Bbb Z$
67272
Deduce that if $G$ is a finite $p$-group, the number of subgroups of $G$ that are not normal is divisible by $p$
77221
Prove that $G$ has a subgroup isomorphic to $G/H$.
117744
$p$-Sylow in quotient groups
13761
Automorphisms in $\mathbb{Z}_n$
3203
Quotient group $\mathbb Z^n/\ \text{im}(A)$
146760
Prove that H is a subgroup of G
45310
If $H\leq Z (G)$ and $G/H$ is nilpotent, then $G$ is nilpotent.
43058
If $n > 2$, prove that the order of the multiplicative group of units modulo n, $U_n$, is even.