On soluble groups in which commutators have prime power order

The article deals with finite groups in which commutators have prime power order (CPPO-groups). We show that if G is a soluble CPPO-group, then the order of the commutator subgroup G ' is divisible by at most two primes. This improves an earlier result saying that the order of the commutator subgroup G ' is divisible by at most three primes.