p-group of class 2 with cyclic commutator subgroup

Question

I was reading a paper "ON THE EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER TWO IN FINITE 2-GROUPS" you can get it from here.
In Introduction page 2 He said "It is worth mentioning here that we need only treat the challenging case where p = 2 because it is well known that every finite p-group, p odd, with cyclic commutator subgroup is regular" and reference to two papers.
1. On finite p-groups with cyclic commutator subgroup, you can get it from here.
2. Finite p-groups with a cyclic commutator subgroup, you can get it from here.
But I can't get from this two papers that how p-group with odd p and cyclic commutator subgroup is regular