Klein Four-Group
/ˈklaɪn fɔːr ɡruːp/noun
A group in abstract algebra containing four elements, in which every nonidentity element has order two.
Did you know?The Klein four-group is isomorphic to the symmetries of a rectangle, excluding reflections across its diagonals, and is written mathematically as C₂ × C₂.
Etymological Timeline
Proto-Germanic / Early Germanic
Proto-Germanic
*klainaz
“Small or slender; the probable ancestral form behind German klein, though the deeper root is uncertain.”
Middle High German
Middle High German
klein
“Small, slight, or fine.”
Modern German
German
klein
“Small; the surname Klein literally means “small” or “little.””
17th Century
French / Italian
groupe / gruppo
“A cluster or assemblage; the source of the mathematical term group.”
19th Century
English
group
“A set of objects considered together; later, a set equipped with a formal algebraic operation.”
1884
German
Vierergruppe
“Felix Klein’s “four-group,” a four-element algebraic structure later known internationally as the Klein four-group.”
Modern English
English
Klein four-group
“The four-element group in which the identity and three other elements each have order two.”