## Compositions of Isomorphisms

We show that the composition of two isomorphisms is again an isomorphism.

## Homomorphisms Preserve Commutativity

We show that the image of an Abelian group under a homomorphism is itself an Abelian group. That is, homomorphisms preserve commutativity.

## A Direct Product Preserves Commutativity

We show that the direct product of two groups is commutative if and only if each of the groups are commutative.

## Subgroups of the Permutations on Three Elements

Here we find all subgroups of set of permutations on three elements. Furthermore, we find the cosets of these and determine which are normal.

## Congruence Modulo n

We show that congruence modulo n is a congruence relation on the set of integers with respect to both addition and multiplication. We also find the kernel of this relation.