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Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Related concepts
The direct product group of the group of order 2 with itself is known as the Klein four group:
Besides the cyclic group of order 4 , the Klein group is the only other group of order 4, up to isomorphism . (This follows, for instance, by thefundamental theorem of finitely generated abelian groups, as in this example).
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
Last revised on October 24, 2020 at 13:20:13. See the history of this page for a list of all contributions to it.