The RandomElement( G ) command returns a randomly selected element of the group G.

The RandomInvolution( G ) command returns a randomly selected involution (element of order $2$) of the group G. An exception is raised if G has odd order (as in that case, G contains no involutions).

For a prime number p, the RandomPElement( p, G ) command returns a random element of the group G with order equal to a power of p. An exception is raised in case p does not divide the order of G.

For a prime number p, the RandomPPrimeElement( p, G ) command returns a random element of the group G with order relatively prime to p. An exception is raised if G is a $p$-group.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$G≔\mathrm{Group}\left(\left\{\mathrm{Perm}\left(\left[\left[1\,2\right]\right]\right)\,\mathrm{Perm}\left(\left[\left[1\,2\,3\right]\,\left[4\,5\right]\right]\right)\right\}\right)$

$G≔⟨\left(1\,2\,3\right)\left(4\,5\right)\,\left(1\,2\right)⟩$

$\mathrm{RandomElement}\left(G\right)$

$\left(1\,2\right)$

$\mathrm{RandomElement}\left(G\right)$

$\left(1\,3\,2\right)$

$G≔\mathrm{ExceptionalGroup}\left(''G2(3)''\right)$

$G≔G_2\left(3\right)$

$\mathrm{RandomInvolution}\left(G\right)\:$

$g≔\mathrm{RandomInvolution}\left(G\right)\:$

$g\∈G$

$\mathrm{true}$

$\mathrm{PermOrder}\left(g\right)$

$2$

$G≔\mathrm{QuasicyclicGroup}\left(5\,\'\mathrm{form}\'\=''multiplicative''\right)$

$G≔C_{5^{\mathrm{\∞}}}$

$g≔\mathrm{RandomElement}\left(G\right)$

$g≔{\ⅇ}^{\frac{4085198}{9765625}\mathrm{I}\mathrm{\π}}$

$g\∈G$

$\mathrm{true}$

$G≔\mathrm{DihedralGroup}\left(5\right)$

$G≔{\mathbf{D}}_5$

$g≔\mathrm{RandomPElement}\left(5\,G\right)$

$g≔\left(1\,5\,4\,3\,2\right)$

$g\∈G$

$\mathrm{true}$

$\mathrm{PermOrder}\left(g\right)$

$5$

$g≔\mathrm{RandomPPrimeElement}\left(5\,G\right)$

$g≔\left(1\,4\right)\left(2\,3\right)$

$g\∈G$

$\mathrm{true}$

$\mathrm{PermOrder}\left(g\right)$

$2$

$G≔\mathrm{DihedralGroup}\left(120\right)\:$

{ to 100 do PermOrder( RandomPElement( 2, G ) ) end };

$\left\{2\,4\,8\right\}$

{ to 100 do PermOrder( RandomPPrimeElement( 2, G ) ) end };

$\left\{3\,5\,15\right\}$

{ to 100 do PermOrder( RandomInvolution( G ) ) end };

$\left\{2\right\}$

The GroupTheory[RandomElement] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.

The GroupTheory[RandomInvolution], GroupTheory[RandomPElement] and GroupTheory[RandomPPrimeElement] commands were introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.