# Definition:Klein Four-Group

## Group Example

The Klein $4$-group, often denoted $K_4$, is a group of $4$ elements, each of which is self-inverse.

### Cayley Table

The Cayley table for $K_4$ is as follows:

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

## Also known as

The Klein four-group (or Klein's four-group) is also known as the four-group or the Viergruppe.

Hence it is often denoted $V$.

The term is often not hyphenated: four group.

Some sources refer to it as the dihedral group of order $4$.

## Also see

• Results about the Klein four-group can be found here.

## Source of Name

This entry was named for Felix Christian Klein.

## Internationalization

Four-group is translated:

 In German: Viergruppe (literally: four-group)