# 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:

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

## Also known as

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

## Internationalization

Four-group is translated:

 In German: Viergruppe (literally: four-group)

## Source of Name

This entry was named for Felix Christian Klein.