Prove that a group where $(ab)^i = a^ib^i$ for $3$ consecutive integers, is abelian
7015
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
18415
Direct sum of Abelian groups and Isomorphism
76317
Let $C$ be the commutator subgroup of $G$. Prove that $G/C$ is abelian
58108
The alternating group is generated by three-cycles
96169
$n$ divides a product of $n$ consecutive integers (by $n$ divides one of them)
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.
108213
$N_1,N_2,N_3 \unlhd G, N_i\cap N_j =\{e\}, G = N_iN_j$. Want to show that $G$ is abelian, $N_i$ are isomorphic.
45760
if G is generated by {a,b} and ab=ba, then prove G is Abelian
7034
Prove that $A+I$ is invertible if $A$ is nilpotent
50266
In the following figure prove that: $AK||BC$
71420
Prove that a group is abelian.
108309
An example of a non-abelian group of order $p^3$
92430
Show that the group is cyclic.
90332
Prove that that $U(n)$ is an abelian group.
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
108425
Problem on abelian group
150585
Group with $a=a^{-1}$ for all $a\in G$ is abelian