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Periodic Sequences of p-Class Tower Groups

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DOI: 10.4236/jamp.2015.37090    2,394 Downloads   2,566 Views   Citations
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ABSTRACT

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.

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Mayer, D. (2015) Periodic Sequences of p-Class Tower Groups. Journal of Applied Mathematics and Physics, 3, 746-756. doi: 10.4236/jamp.2015.37090.

References

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