Overview
Group theory is the study of the mathematical structure of groups. It is used in various areas of mathematics, and is of particular importance in the study of symmetry, especially in Physics.
Axioms
A group is a set {% G %} equipped with a binary operation that satisfies 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 %}