New posts in Abelian Groups

Let $G$ be a group in which $aba = b \; \forall a,b \in G$. Prove that $G$ is Abelian.

Is every direct product of (finite) cyclic groups abelian?

Give a reason why $\mathbb Z_{64}\times \mathbb Z_4$ and $\mathbb Z_{64}\times \mathbb Z_{2}\times \mathbb Z_{2}$ are not isomorphic.

Elements of the same order in the same conjugacy class that commute are contained in the same cyclic subgroup

Let $G$ be a finite abelian group, and let $n$ divide $|G|$. Let $m$ be the number of solutions of $x^n=1$. Prove that $n\mid m$.

Abelian finite groups and their subgroups

Does there exist an operation that could turn the set of all negative real numbers into an abelian group?

If $G$ is not abelian, then $\#\text{Inn}(G) \geq 4$

The existence of group isomorphism between Euclidean space.

Grothendieck group "commutes" with direct sum