If I have a group created by the set of generators and an element of this
group, how can I express this element via this particular set of generators
For example, if we look on the example of analysing Rubic's Cube at GAP
we create a group by 6 permutations, and then for every state of puzzle we
perform membership test. In this case representing of the permutation via
that 6 generators means solving the puzzle.
Alexander B. Konovalov,
Zaporozhye State University, Zaporozhye, Ukraine