Definition:Klein Four-Group

Definition
The Klein four-group is a group of four elements, each of which is self-inverse.

Its Cayley table is given by:


 * $\begin{array}{c|cccccc}

& e & a & b & c \\ \hline e & e & a & b & c \\ a & a & e & c & b \\ b & b & c & e & a \\ c & c & b & a & e \\ \end{array}$

Alternative Names
The Klein four-group is also known as the four-group or the Viergruppe.