Klein four-group

- group, ∞-group
- group object, group object in an (∞,1)-category
- abelian group, spectrum
- group action, ∞-action
- representation, ∞-representation
- progroup
- homogeneous space

The direct product group of the group of order 2 with itself is known as the *Klein four group*:

$\mathbb{Z}/2 \times \mathbb{Z}/2
\,.$

Besides the cyclic group of order 4 $\mathbb{Z}/4$, the Klein group $\mathbb{Z}/2 \times \mathbb{Z}/2$ is the only other group of order 4, up to isomorphism.

In particular the Klein group is *not* itself a cyclic group, and it is in fact the smallest non-trivial group which is not a cyclic group.

In the ADE-classification of finite subgroups of SO(3), the Klein four-group is the smallest in the D-series, labeled by D4.

**ADE classification** and **McKay correspondence**

See also

- Wikipedia,
*Klein four-group*

Last revised on August 29, 2019 at 10:11:42. See the history of this page for a list of all contributions to it.