Definition:Klein Four-Group
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Definition
The Klein four-group is a group of four elements, each of which is self-inverse.
Its Cayley table is given by:
- $\begin{array}{c|cccccc} & e & a & b & c \\ \hline e & e & a & b & c \\ a & a & e & c & b \\ b & b & c & e & a \\ c & c & b & a & e \\ \end{array}$
Also known as
The Klein four-group is also known as the four-group or the Viergruppe.
Internationalization
Four-group is translated:
In German: | Viergruppe | (literally: four-group) |
Source of Name
This entry was named for Felix Christian Klein.
Sources
- Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 25$
- Richard A. Dean: Elements of Abstract Algebra (1966)... (previous)... (next): $\S 1.5$: Example $15$
- Allan Clark: Elements of Abstract Algebra (1971)... (previous)... (next): $\S 26 \iota$
- Thomas W. Hungerford: Algebra (1974)... (previous)... (next): $\text{I}$: Groups: $\S 1$: Semigroups, Monoids and Groups: Exercise $6$
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 44.5$