Group theory Study Group

A group is a set of things together with an operation that lets you combine them, as long as four rules hold.
The basic idea:

> A group is a collection of transformations where you can combine transformations, undo them, and still stay inside the same system.

Classic example: rotating a square.
You can rotate a square by:

• 0°
• 90°
• 180°
• 270°

If you rotate 90° and then 180°, that is the same as rotating 270°. You are still within the same set of rotations. Every rotation has an undoing rotation. That structure forms a group.

During this meeting, we will be looking at its formulation, definitions, and some examples.