New posts in Direct Product

The only group $G$ with one $A$ and one $B$ as composition factors is $G = A\times B$ (where $A$ and $B$ are non-abelian, finite and simple)

Homomorphisms from $\prod_{i\in\mathbb Z}\mathbb Z $ to $\oplus_{i\in\mathbb Z}\mathbb Z$ that fixes $\oplus_{i\in\mathbb Z}\mathbb Z$

If $A$ and $B$ are groups then prove that $A\times B\cong B\times A$

Does there exist a group that is both a free product and a direct product of nontrivial groups?

In the category $\mathbf{Set}$ is "the product of an empty set of sets a one-element set"?

Structure of groups of order $pq$, where $p,q$ are distinct primes.

Direct sums and direct products