Group Presentations

Groups can be represented by generators and relations, which are products of generators and their inverses that yield the identity element. This representation is called a presentation of a group and describes it completely. Conversely, however, it is generally not possible to decide from two given presentations whether they describe the same group or not. This leads us to the decision problems, first formulated by Max Dehn, which can be solved in many cases in a very geometric way as described in Chap. 10 .