If $|G|=24$ or $48,36,56,72,80,90$ or $96$ prove that $G$ is an abelian or simple group .
92899
$G$ is non abelian simple group of order $<100$ then $G\cong A_5$
103216
The set $\{g^2 | g \in G\}$ in a group $G$
6153
Suppose that $G$ is a group with the property that for every choice of elements in $G$, $axb=cxd$ implies $ab=cd$. Prove that $G$ is Abelian.
5297
If G is a finite abelian group and $a_1,...,a_n$ are all its elements, show that $x=a_1a_2a_3...a_n$must satisfy $x^2=e$.
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
60208
Proof of property of abelian group
78048
Group of order 24 with no element of order 6 is isomorphic to $S_4$
151025
If G is a group of order n=35, then it is cyclic
83938
If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
57421
If $\forall x \in G$ where G is a group $x=x^{-1}$ then how is this group abelian?
7079
ord $(b)|\max\{\text{ord}(g)|g\in G\}$ for all $b\in G\,$ a finite abelian group
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
102429
There are 2 groups of order 6 (up to isomorphism)
90811
If $[G' : G'']\leq p^2$, then $G'$ is abelian.
17510
Proving a set is an abelian group.
13631
Showing group with $p^2$ elements is Abelian
127603
If $G$ be a group of order $8$ and $x$ be a element of order $4$. Prove that $x^2 \in Z(G)$