Prove that a group of order $p^2$ where $p$ is prime is Abelian.
13631
Showing group with $p^2$ elements is Abelian
65900
Show that a finite group with certain automorphism is abelian
28722
Prove that $H$ is a abelian subgroup of odd order
63499
Groups of prime squared order
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
103423
Normal subgroup where G has order prime
115427
Galois group of $\prod_{i=1}^{p-1} (X^2-i)$
79995
G is group of order pq, pq are primes
106577
If G is not abelian with order $p^3$ then $G'=Z(G)$
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
74964
Showing Galois Group is Abelian
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
59128
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
15633
If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$.
134820
$p$ prime, Group of order $p^n$ is cyclic iff it is an abelian group having a unique subgroup of order $p$
57427
Group of order $8p$ is solvable, for any prime $p$