Proof that a finite abelian group has a subgroup of order $n$ for every $n$ which divides $|G|$
24966
Converse of Lagrange's theorem for abelian groups
133770
Subgroups of finite abelian groups.
17178
Order of $\phi(g)$ divides the order of $g$
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
37913
Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
21673
If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
152662
Proving that any finite cyclic group of order $n$ is isomorphic to $$
150156
Proving that $S_n$ has order $n!$
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
12667
How many subgroups of order $n$ does $D_n$ have?
134820
$p$ prime, Group of order $p^n$ is cyclic iff it is an abelian group having a unique subgroup of order $p$
145406
Prove every element of $G$ has finite order.
126893
A group of order 2p (p prime) and other conditions - prove abelian.
26624
Prove that is group is abelian
71420
Prove that a group is abelian.
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$