Isomorphism-invariants and their applications in testing for isomorphism between finitely presented groups

This paper introduces some isomorphism-invariants for groups and uses them to test two finitely presented groups. The introduced algorithm starts with the construction of all cyclic groups contained in the groups under test, then it compares the distribution of a particular set of elements in the constructed cyclic groups. The algorithm leads to one of these two results: 1. The groups have the same "fingerprint" 2. The groups are not isomorphic