Gapplet
Given a set of permutations of {1, ..., n} generating the subgroup G of Sn, determine the order of G by means of stabilizer and orbit computation.
Give a sequence of generators for G,
e.g., (1,2,3)(4,5,6), (2,3)(5,6), (1,4)(2,5)(3,6)(7,8) |
|
We apply the algorithm and compute
the length of the
orbit containing 1 and the order of its stabilizer, and multiply the
two numbers to obtain the order of G.
| |
The procedure for the order determination of a permutation group is recursive; therefore we do not show how the order of the stabilizer is computed. See a previous gapplet for the full treatment.