Definition:Cyclic Permutation/Also known as

Cyclic Permutation: Also known as

A cyclic permutation of length $k$ is also known as:

a cycle of length $k$

a $k$-cycle

generally, just a cycle.

Some sources give it as circular permutation.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 8$: Compositions Induced on Subsets
• 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 1.6$: Exercise $4.5$
• 1968: Ian D. Macdonald: The Theory of Groups ... (previous) ... (next): Appendix: Elementary set and number theory
• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Symmetric Groups: $\S 79$
• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $9$: Permutations: Definition $9.2$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): circular permutation
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cyclic permutation (circular permutation)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): circular permutation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cyclic permutation (circular permutation)