A definition of group
Topics
About: group
The table of contents of this article
Starting Context
- The reader knows a definition of set.
Target Context
- The reader will have a definition of group.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Definition
Any set, S, with any binary operation (called 'group operation'), \(\bullet: S \times S \rightarrow S\), such that for any elements, \(p_1, p_2, p_3 \in S\), 1) \((p_1 \bullet p_2) \bullet p_3 = p_1 \bullet (p_2 \bullet p_3)\); 2) \(i \in S\) (called 'identity element') such that \(i \bullet p_1 = p_1 \bullet i = p_1\); 3) \(p_1^{-1} \in S\) (called 'inverse element of \(p_1\)') such that \(p_1^{-1} \bullet p_1 = p_1 \bullet p_1^{-1} = i\)
