  Geometric methods proposed by Stallings for treating finitely generated
subgroups of free groups were successfully used to solve a wide collection of
decision problems for free groups and their subgroups.
  It turns out that Stallings' methods can be effectively generalized for the
class of amalgams of finite groups. In the present paper we employ subgroup
graphs constructed by the generalized Stallings' folding algorithm to solve
various algorithmic problems in amalgams of finite groups.
