title: Is a given set of group elements a set of coset representatives?
body: <p>I am afraid the question is a bit technical, but I hope someone might have stumbled into a similar subject, or give me a pointer of some kind.</p>
  
  <p>If G is a group (in the sense of algebraic structure), and if g<sub>1</sub>, ..., g<sub>n</sub> are elements of G, is there an algorithm (or a function in some dedicated program, like GAP) to determine whether there is a subgroup of G such that those elements form a set of representatives for the cosets of the subgroup? (We may assume that G is a permutation group, and probably even the full symmetric group.)</p>
  
  <p>(There are of course several algorithms to find the cosets of a given subgroups, like Todd-Coxeter algorithm; this is a kind of inverse question.)</p>
  
  <p>Thanks,
  Daniele</p>