The Intersection( A, B, ... ) command computes the intersection of one or more permutation groups A, B, ...

You can also compute the intersection of two permutation groups A and B by using the intersect operator: A intersect B.

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

$A≔\mathrm{Group}\left(\mathrm{Perm}\left(\left[\left[1\,13\,7\,24\,2\,17\,4\,19\right]\,\left[3\,5\,9\,23\,8\,15\,10\,22\right]\,\left[6\,14\,11\,21\,12\,18\,16\,20\right]\right]\right)\right)$

$A≔⟨\left(1\,13\,7\,24\,2\,17\,4\,19\right)\left(3\,5\,9\,23\,8\,15\,10\,22\right)\left(6\,14\,11\,21\,12\,18\,16\,20\right)⟩$

$B≔\mathrm{Group}\left(\mathrm{Perm}\left(\left[\left[1\,14\,7\,21\,2\,18\,4\,20\right]\,\left[3\,6\,9\,11\,8\,12\,10\,16\right]\,\left[5\,13\,23\,24\,15\,17\,22\,19\right]\right]\right)\right)$

$B≔⟨\left(1\,14\,7\,21\,2\,18\,4\,20\right)\left(3\,6\,9\,11\,8\,12\,10\,16\right)\left(5\,13\,23\,24\,15\,17\,22\,19\right)⟩$

$\mathrm{GroupOrder}\left(A\right)\,\mathrm{GroupOrder}\left(B\right)$

$8,8$

$H≔A\∩B$

$H≔⟨\left(1\,7\,2\,4\right)\left(3\,9\,8\,10\right)\left(5\,23\,15\,22\right)\left(6\,11\,12\,16\right)\left(13\,24\,17\,19\right)\left(14\,21\,18\,20\right)⟩$

$\mathrm{GroupOrder}\left(H\right)$

$4$

$\mathrm{Intersection}\left(H\right)$

$⟨\left(1\,7\,2\,4\right)\left(3\,9\,8\,10\right)\left(5\,23\,15\,22\right)\left(6\,11\,12\,16\right)\left(13\,24\,17\,19\right)\left(14\,21\,18\,20\right)⟩$

$A≔\mathrm{Group}\left(\mathrm{Perm}\left(\left[\left[2\,4\right]\,\left[3\,5\right]\right]\right)\,\mathrm{Perm}\left(\left[\left[2\,4\,6\right]\right]\right)\right)$

$A≔⟨\left(2\,4\right)\left(3\,5\right)\,\left(2\,4\,6\right)⟩$

$B≔\mathrm{Group}\left(\mathrm{Perm}\left(\left[\left[1\,3\right]\,\left[2\,6\right]\right]\right)\,\mathrm{Perm}\left(\left[\left[2\,6\,4\right]\right]\right)\right)$

$B≔⟨\left(1\,3\right)\left(2\,6\right)\,\left(2\,6\,4\right)⟩$

$C≔\mathrm{Group}\left(\mathrm{Perm}\left(\left[\left[1\,3\right]\,\left[2\,4\right]\right]\right)\,\mathrm{Perm}\left(\left[\left[2\,6\,4\right]\right]\right)\right)$

$C≔⟨\left(1\,3\right)\left(2\,4\right)\,\left(2\,6\,4\right)⟩$

$J≔\mathrm{Intersection}\left(A\,B\,C\right)$

$J≔⟨\left(2\,4\,6\right)⟩$

$\mathrm{GroupOrder}\left(J\right)$

$3$

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

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