Group Theory
Overview
Axioms
A group is a set {% G %} equipped with a binary operation that satifies the following axioms.
- closure - for each pair of object in the group, a and b, then a * b is a member of the group
- associativity - a*(b*c) = (a*b)*c
- identity - there is an element e such that e*a = a and a*e = a for any element of the group, a
- inverse - for each element of the group a, there is an element {% a^{-1} %} such that {% a * a^{-1} = e %}
Examples of Groups
- Real numbers with the operation of multiplication
- Rotations in the plane, with composition (one rotation followed by another as a single rotation)
Additional Topics
