Finitely presented periodic group

Definition
A group is termed a finitely presented periodic group if it satisfies both the following conditions:


 * 1) It is a finitely presented group -- it has a presentation that uses a finite number of generators and a finite number of relations.
 * 2) It is a periodic group -- every element has finite order.

Conjecture
The conjecture that every finitely presented periodic group is finite is currently open. Note that there do exist finitely generated periodic groups that are not finite, such as the Grigorchuk group and Tarski monsters and other negative solutions to the Burnside problem (see periodic not implies locally finite).