Locally finite groups with small element orders

A. Mamontov

The spectrum of a periodic group is the set of its element orders. Obviously, the spectrum of a group \(G\) is finite if and only if the exponent of \(G\) is finite. So, there are groups with finite spectrum that are not locally finite. We discuss results on spectrum that ensure the local finiteness of a corresponding group and examples of groups which can be recognized by spectrum in the class of periodic (not necessarily finite) groups.