Recent examples of periodic bifurcations in descendant trees of finite p-groups with ?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) , ...Recent examples of periodic bifurcations in descendant trees of finite p-groups with ?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 , resp. . 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.展开更多
文摘Recent examples of periodic bifurcations in descendant trees of finite p-groups with ?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 , resp. . 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.
