is finitely generated (respectively finitely related, ') if it has a presentation that is finitely generated (respectively finitely related, a finite presentation). A group which has a finite presentation with a single relation is called a one-relator group.

Recursively presented groups

If S is indexed by a set I consisting of all the natural numbers N or a finite subset of them, then it is easy to set up a simple one to one coding (or Gödel numbering)

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