If $(G,*)$ is an abelian group, then show that $(a * b)^n = a^n * b^n$.
32735
If $ \langle G, \star \rangle $ is an abelian group, then for all $a, b \in G$, show that $(a \star b)^{n} = a^{n} \star b^{n}$.
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
135039
${\rm Aut}(G)$ is cyclic $\implies G$ is abelian
156429
If $G$ is a group whereby $(a\cdot b)^{i} =a^i\cdot b^i$ for three consecutive integers $i$ for all $a, b \in G$, show $G$ is abelian.
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
27905
Let $G$ be a group, where $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5$. Prove that $G $ is an abelian group.
17510
Proving a set is an abelian group.
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
113936
Showing that a finite abelian group has a subgroup of order m for each divisor m of n
158074
Cyclic group $G$ with generator $ab$.
88995
Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.