Анотація:
We investigate properties of groups with subgroups of finite exponent and prove that a non-perfect group G of infinite exponent with all proper subgroups of finite exponent has the following properties:
(1) G is an indecomposable p-group,
(2) if the derived subgroup G′ is non-perfect, then G/G′′ is a group of Heineken-Mohamed type.
We also prove that a non-perfect indecomposable group G with the non-perfect locally nilpotent derived subgroup G′ is a locally finite p-group.