‘Groups’ Underpin Modern Math. Here’s How They Work

Figuring out what subgroups a group contains is one way to understand its structure. For example, the subgroups of Z₆ are {0}, {0, 2, 4} and {0, 3}—the trivial subgroup, the multiples of 2, and the multiples of 3. In the group D₆, rotations form a subgroup, but reflections don’t. That’s…