Transitivity - Maple Help

GroupTheory

 Transitivity
 compute the transitivity of a permutation group

 Calling Sequence Transitivity( G )

Parameters

 G - a permutation group

Description

 • The transitivity of a permutation group $G$ is the largest non-negative integer $k$ for which $G$ is $k$-transitive. In other words, the transitivity of $G$ is $k$ if $G$ is $k$-transitive, but not $\left(k+1\right)$-transitive. (By convention, the transitivity of an intransitive group is equal to $0$.)
 • The Transitivity( G ) command returns the transitivity of the permutation group G. The group G must be an instance of a permutation group.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $\mathrm{Transitivity}\left(\mathrm{Alt}\left(4\right)\right)$
 ${2}$ (1)
 > $\mathrm{Transitivity}\left(\mathrm{Symm}\left(4\right)\right)$
 ${4}$ (2)
 > $\mathrm{Transitivity}\left(\mathrm{Alt}\left(5\right)\right)$
 ${3}$ (3)
 > $\mathrm{Transitivity}\left(\mathrm{Symm}\left(5\right)\right)$
 ${5}$ (4)
 > $\mathrm{Transitivity}\left(\mathrm{MathieuGroup}\left(23\right)\right)$
 ${4}$ (5)

Compatibility

 • The GroupTheory[Transitivity] command was introduced in Maple 2016.