Periodic solvable group

Definition
A group is termed a periodic solvable group or locally finite solvable group if it satisfies the following equivalent conditions:


 * 1) It is both a locally finite group (every finitely generated subgroup is finite) and a solvable group (the derived series reaches the trivial subgroup in finitely many steps).
 * 2) It is both a periodic group (every element has finite order) and a solvable group (the derived series reaches the trivial subgroup in finitely many steps).
 * 3) It is a solvable group and all the groups obtained by taking quotients of successive members of its derived series are periodic abelian groups.