Subgroups Part 1

A subgroup is a subset of a group that with the restricted composition table inherited from the parent group satisfies the axioms of group theory as follows:

The subgroup’s restricted composition table must be closed and only contain elements of the subgroup.

The identity must be within the subgroup.

Associativity will be effortlessly inherited from the parent group.

For all elements within the subgroup, their inverse must also be in the subgroup.


In this video we explain this definition in detail and then go through some examples.

One of the examples we look at is the subgroups of the group of integers under addition. We find all the possible subgroups of this group and show how all but the trivial subgroup are isomorphic to the original group.