Group Theory

The animation visualizes the group of hexagon rotations (ℤ₆) by showing how adding rotation steps works modulo 6, verifying the four group axioms, and demonstrating valid subgroups like {0, 2, 4} versus invalid sets like {0, 1}. It concludes by illustrating Lagrange's theorem, which states that the size of any subgroup must divide the size of the whole group.