Suppose a group G is generated by two elements a and b. If ab=ba, prove that G is abelian.
45760
if G is generated by {a,b} and ab=ba, then prove G is Abelian
74964
Showing Galois Group is Abelian
125345
Suppose $a$ and $b$ are group elements, $a$ and $b$ commute, $|a|$ and $|b|$ are both finite. What are the possibilities for $|ab|$?
90332
Prove that that $U(n)$ is an abelian group.
65900
Show that a finite group with certain automorphism is abelian
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
43783
Abelian group (Commutative group)
70394
Prove that $a * b$ is a group (Hungerford, 2nd ed., sec $7.2$, Exercise $22$)
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
71232
if $A$ is Abelian group , $B$ is subgroup of $A$ , Is $B \times A/B \cong A$?
1364
Let $G$ be a group in which $a^2=e$ for all elements of $a$ of $G$. Show that $G$ is Abelian.
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
158074
Cyclic group $G$ with generator $ab$.
98542
Prove that $H$ is a subgroup of an abelian group $G$
108425
Problem on abelian group
140334
Let $G$ be a group and $H$ be a subgroup of $G$ of index $2$ .Then show that if $a,b\notin H$ then $ab\in H$.