Let G be a finite group, $|G| = 1575$ and suppose $n_3 =1$. Prove $G$ is abelian
65926
Group of order $1575$ having a normal sylow $3$ subgroup is abelian.
84789
Order of products of elements in a finite Abelian group
85579
$G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$
90332
Prove that that $U(n)$ is an abelian group.
45760
if G is generated by {a,b} and ab=ba, then prove G is Abelian
83938
If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
59007
Suppose $|G| = 105$. Show that it is abelian if it has a normal $3$-Sylow subgroup.
65613
$G$ is a finite group and $T$ an automorphism of $G$ such that $T$ sends more than $\frac{3}{4}|G|$ elements to their inverse.
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
98542
Prove that $H$ is a subgroup of an abelian group $G$
7015
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
125559
In a group $G$, if for all $a,b,c\in G$, $ab=ca\Rightarrow b=c$, then $G$ is abelian
59128
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
139100
A question on the group algebra $k[G]$ of a finite abelian group
57809
For which $n$, $G$ is abelian?
113936
Showing that a finite abelian group has a subgroup of order m for each divisor m of n
13355
Product of elements of a finite abelian group