**Appendix A**
Addendum for Chapter 1

# A.1 Groups and special relativity

## A.1.1 Fundamentals of group theory

### Properties of groups

A group is a set of elements that have the following properties:

- Contains the identity transformation 1;
- If E and E′ are elements in the group, then there exists a group operation (generically called “multiplication”) that always produces an element of the group, E″ ≡ E′ · E (closure);
- For every transformation element E, there exists in the group an inverse element E
^{−1}, where E^{−1}· E = 1;
- The group operation is associative, E″ · (E′ · E) = (E″ · E′)· E.

A particular type of group satisfies an additional property. For an abelian group, the group operation yields the same answer regardless of the order, E′ · E = E · E′. ...