  Recent examples of periodic bifurcations in descendant trees of finite
p-groups with p in {2,3} are used to show that the possible p-class tower
groups G of certain multiquadratic fields K with p-class group of type (2,2,2),
resp. (3,3), form periodic sequences in the descendant tree of the elementary
abelian root C(2)xC(2)xC(2), resp. C(3)xC(3). The particular vertex of the
periodic sequence which occurs as the p-class tower group G of an assigned
field K is determined uniquely by the p-class number of a quadratic, resp.
cubic, auxiliary field k, associated unambiguously to K. Consequently, the hard
problem of identifying the p-class tower group G is reduced to an easy
computation of low degree arithmetical invariants.
