# Finitely generated not implies finitely presented

From Groupprops

This article gives the statement and possibly, proof, of a non-implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., finitely generated group) neednotsatisfy the second group property (i.e., finitely presented group)

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## Statement

There exists a finitely generated group that is not finitely presented, i.e., it has *no* presentation with finitely many generators and finitely many relations.

## Proof

### Example of the wreath product of group of integers with group of integers

`Further information: Wreath product of group of integers with group of integers`