What Is a Group?

Four simple rules

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

• A group: closure, associativity, an identity and inverses.
• Symmetries, clock arithmetic and integer addition are all groups.
• Abelian groups are commutative. The triangle’s 6 symmetries are the smallest non-abelian group.

Steps

1. The rules
2. Integers and addition
3. Group or not?
4. A multiplicative inverse
5. Undo a turn
6. Commutative or not