nLab
cyclic permutation
Contents
Context
Group Theory
group theory

Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Contents
Definition
For a finite set $X$ , a cyclic permutation on $X$ is a permutation $\sigma \colon X \to X$ such that the induced group homomorphism $\mathbb{Z} \to Aut(X)$ from the integers to the automorphism group (i.e. the symmetric group ) of $X$ , sending $n \in \mathbb{Z}$ to $\sigma^n$ , defines a transitive action .

One may visualize the elements of $X$ as points arranged on a circle spaced equally apart, with $\sigma(x)$ the next-door neighbor of $x$ in the counterclockwise direction, hence the name.

See also rotation permutation .

Last revised on December 31, 2018 at 07:16:13.
See the history of this page for a list of all contributions to it.