Definition:Even Permutation

Definition

Let $n \in \N$ be a natural number.

Let $S_n$ denote the symmetric group on $n$ letters.

Let $\rho \in S_n$ be a permutation in $S_n$.

$\rho$ is an even permutation if and only if:

$\map \sgn \rho = 1$

where $\sgn$ denotes the sign function.

Also see

• Definition:Odd Permutation

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 7.4$. Kernel and image: Example $142$
• 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: $\S 81$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): even permutation