Definition:Klein Four-Group/Also known as
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Klein Four-Group: 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::
Some sources refer to it as the dihedral group of order $4$.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $25$. Cyclic Groups and Lagrange's Theorem
- 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 1.5$: Example $15$
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Definition of Group Structure: $\S 26 \iota$
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 44$ Some consequences of Lagrange's Theorem
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): four group
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $3$: Elementary consequences of the definitions: Groups with four elements
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): four group
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Klein's four group
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): four-group