Infinitely Presented, Finitely Generated Group

[markiv]

What's an example of a group that has finitely many generators, but cannot be presented using only finitely many relations? Are there any nice groups? They do exist, right?

 

[DonAntonio]

What's an example of a group that has finitely many generators, but cannot be presented using only finitely many relations? Are there any nice groups? They do exist, right?

http://caissny.org/pdfs/A%20finitely%20generated,%20infinitely%20related%20group%20with%20trival%20multiplicator.PDF

I cannot say how nice this group is, but it doesn't look that evil.

DonAntonio