Degree - Maple Help

GroupTheory

 Degree
 return the degree of a permutation group

 Calling Sequence Degree( G )

Parameters

 G - a permutation group

Description

 • The degree of a permutation group is the cardinality of the set upon which it acts.  Since permutation groups act on sets of the form $\left\{1,2,\dots ,n\right\}$, the degree is the positive integer $n$.
 • The Degree( G ) command returns the degree of a permutation group G.
 • Some group constructors, such as those for the symmetric and alternating groups take a degree parameter as input, and the Degree command returns this value.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{Group}\left(\mathrm{Perm}\left(\left[\left[1,2\right]\right]\right),\mathrm{Perm}\left(\left[\left[2,3,4\right]\right]\right)\right)$
 ${G}{≔}⟨\left({1}{,}{2}\right){,}\left({2}{,}{3}{,}{4}\right)⟩$ (1)
 > $\mathrm{Degree}\left(G\right)$
 ${4}$ (2)
 > $\mathrm{Degree}\left(\mathrm{DihedralGroup}\left(14\right)\right)$
 ${14}$ (3)
 > $\mathrm{Degree}\left(\mathrm{AlternatingGroup}\left(10\right)\right)$
 ${10}$ (4)

Compatibility

 • The GroupTheory[Degree] command was introduced in Maple 17.