- group, ∞-group
- group object, group object in an (∞,1)-category
- abelian group, spectrum
- super abelian group
- group action, ∞-action
- representation, ∞-representation
- progroup
- homogeneous space

**Classical groups**

**Finite groups**

**Group schemes**

**Topological groups**

**Lie groups**

**Super-Lie groups**

**Higher groups**

**Cohomology and Extensions**

**Related concepts**

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.

See also:

- Wikipedia,
*Cyclic permutation*

Last revised on April 18, 2021 at 16:19:27. See the history of this page for a list of all contributions to it.