Computing with group homomorphisms (Q1192232)

Based on the elementary remark that a mapping \(\phi\) from a group \(G\) into a group \(H\) is a homomorphism if and only if the set \(\{(g,\phi(g))\mid g\in G\}\) is a subgroup of \(G\times H\), the authors describe simple but highly efficient algorithmic methods for deciding if a mapping \(\phi\) from a generating set \(X\) of \(G\) into \(H\) determines a homomorphism, and in case it does to determine the kernel of that homomorphism. For these methods \(G\) and \(H\) are supposed to be permutation groups or polycyclicly presented groups and standard methods for these classes of groups, like the ``Schreier-Sims method'' and ``base change'' for permutation groups or the ``non-commutative Gauß Algorithm'' for polycyclic groups, are employed.