How to prove that a Group $G$ with order $p^2$ must be a abelian group(where p is a prime)?
13631
Showing group with $p^2$ elements is Abelian
13742
Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
66877
Showing groups of order $p^{k}(p+1)$ are not simple, p prime
121481
Non-abelian finite $p$-group in which every element has prime order?
103423
Normal subgroup where G has order prime
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
19668
Does every group whose order is a power of a prime p contain an element of order p?
108425
Problem on abelian group
122335
Abelian $p$-group with unique subgroup of index $p$
15526
Question on groups of order $pq$
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
38853
Cyclic group of prime order
47239
For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
119512
If H ≤ Z(G) ≤ G, where G is a finite group,Z(G) is its center, and (G:H) = p for some prime p, then G is abelian.
152820
Every element of a group has order $2$. Why, intuitively, is it abelian?
134455
Any group of order $15$ is abelian(without sylow theorem)