  Let V(F_pG) be the group of normalized units of the group algebra F_pG of a
finite nonabelian p-group G over the field F_p of p elements. Our goal is to
investigate the power structure of V(F_pG), when it has nilpotency class p. As
a consequence, we have proved that if G and H are p-groups with cyclic Frattini
subgroups and p>2, then V(F_pG) is isomorphic to V(F_pH) if and only if G and H
are isomorphic.
