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 Klein $4$-group can be described completely by showing its Cayley table:

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


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.

Hence it is often denoted $V$.

The term is not always hyphenated::

Klein four group or Klein's four group
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.


Four-group is translated:

In German: Viergruppe  (literally: four-group)