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arXiv · 2006.09177

Schur sigma-groups with abelian quotient invariants (9,3)

Daniel C. Mayer
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Abstract

By the construction of suitable non-metabelian Schur sigma-groups S of type (9,3) with log order lo(S) = 21 and nilpotency class cl(S) = 9, evidence is provided of a new class of imaginary quadratic fields K with 3-class group Cl(3,K) ~ C(9) * C(3) and punctured principalization type kappa ~ (1,4,4;4) whose 3-class field tower consists of precisely three stages. In contrast, previous examples of three-stage towers were associated with kappa in { (1,1,2;2), (1,1,2;3), (1,1,4;2), (1,2,3;1) }, lo(S) = 9 and cl(S) = 5.

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Daniel C. Mayer. 2020-06-12. Schur sigma-groups with abelian quotient invariants (9,3). https://arxiv.org/abs/2006.09177

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