The Pohlig–Hellman Method Generalized for Group Structure Computation

We present a new algorithm that extends the techniques of the Pohlig–Hellman algorithm for discrete logarithm computation to the following situation: given a finite Abelian group and group elements h , g1, , gl, compute the least positive integer y and numbers x1, , xlsuch that hy = ∏gixi. This computational problem is important for computing the structure of a finite Abelian group.