Order & Lagrange

Counting inside groups

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• The order of an element is how many applications return to the identity.
• Lagrange: subgroup orders, and so element orders, divide the group’s order.
• Every group of prime order is cyclic.

Steps

1. Lagrange’s theorem
2. An impossible element
3. Corner to corner
4. Possible subgroup sizes
5. Subgroups of the clock
6. Prime-sized groups