Algorithmic problems in amalgams of finite groups
by
Luda Markus-Epstein
Technion, Haifa, Israel

It turns out that finitely generated subgroups of amalgams of finite groups can be effectively represented by finite cannonical graphs. These graphs posses all the essensial information about the subgroups, which enables one to use them in order to solve various algorithmic problems: the membership problem, the finite index problem, the conjugacy of subgroups, the freeness problem, the separability problem, the reading of Kurosh decomposition (in the case of free products) and others.

We'll present some problems of the above list and their solutions.

Date received: March 6, 2006