Definition:Klein Four-Group

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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:

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


Subgroups

Klein Four-Group/Subgroups

Also known as

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

The term is often not hyphenated: four group.

Hence it is often denoted $V$.


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)


Sources