3-Class field towers of exact length 3

Bush, Michael R.; Mayer, Daniel C.

doi:10.1016/j.jnt.2014.08.010

Cited by 27 publications

(53 citation statements)

References 17 publications

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“…for selecting among several candidates G for the p-class tower group, in dependence on the torsion-free unit rank of the base field K, for instance in [21] [23].…”

Section: Is a Chain Of Normal Subgroups ( )mentioning

confidence: 99%

Artin Transfer Patterns on Descendant Trees of Finite p-Groups

Mayer¹

2016

APM

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“…for selecting among several candidates G for the p-class tower group, in dependence on the torsion-free unit rank of the base field K, for instance in [21] [23].…”

Section: Is a Chain Of Normal Subgroups ( )mentioning

confidence: 99%

Artin Transfer Patterns on Descendant Trees of Finite p-Groups

Mayer¹

2016

APM

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“…Remmert [268] [14], [215]), Bartholdi [16], Bush [47,48,49], Hajir [107,108], Kuhnt [160], Maire [181,182], D. Mayer [188,189,190,191]), McLeman [193], Nover [231], Steurer [307]. Auch die gruppentheoretische Seite dieses Themenkomplexes wurde ausgiebig untersucht (Magnus [180], Serre [293], Nebelung, [222]).…”

Section: Scholz In Freiburgunclassified

“…In den letzten Jahren haben auch Bush und vor allem D. Mayer [188,189,190,191,49] die Kapitulation in unverzweigten kubischen Erweiterungen und die dazugehöri-gen Klassenkörpertürme ausgiebig untersucht.…”

Section: =unclassified

Der Briefwechsel Hasse - Scholz - Taussky

Hasse¹,

Scholz²,

Taussky³

2016

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“…As we have shown in detail in [6], Proof of Thm. , and three groups of derived length 3 and order in Equation (31) …”

Section: Second P-class Groups With Finite Covermentioning

confidence: 74%

“…Iterated IPADs of second order are used in Section 6 for the indirect calculation of TKTs in Section 6.1, and for determining the exact length ( ) ( [6], Cor.4.1.1), which resisted all attempts up to now. Finally, we emphasize that IPADs of infinite p -class towers reveal an unknown wealth of possible fine structure in Section 7 on complex quadratic fields K having a 3-class group ( ) 3 Cl K of type (3,3,3) .…”

Section: Introductionmentioning

confidence: 99%

Index-<i>p</i> Abelianization Data of <i>p</i>-Class Tower Groups

Mayer¹

2015

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Given a fixed prime number p, the multiplet of abelian type invariants of the p-class groups of all unramified cyclic degree p extensions of a number field K is called its IPAD (index-p abelianization data). These invariants have proved to be a valuable information for determining the Galois group p G 2 of the second Hilbert p-class field and the p-capitulation type  of K. For p 3 = and a number field K with elementary p-class group of rank two, all possible IPADs are given in the complete form of several infinite sequences. Iterated IPADs of second order are used to identify the group p G ∞ of the maximal unramified pro-p extension of K.

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3-Class field towers of exact length 3

Cited by 27 publications

References 17 publications

Artin Transfer Patterns on Descendant Trees of Finite p-Groups

Artin Transfer Patterns on Descendant Trees of Finite p-Groups

Der Briefwechsel Hasse - Scholz - Taussky

Index-<i>p</i> Abelianization Data of <i>p</i>-Class Tower Groups

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3-Class field towers of exact length 3

Cited by 27 publications

References 17 publications

Artin Transfer Patterns on Descendant Trees of Finite p-Groups

Artin Transfer Patterns on Descendant Trees of Finite p-Groups

Der Briefwechsel Hasse - Scholz - Taussky

Index-&lt;i&gt;p&lt;/i&gt; Abelianization Data of &lt;i&gt;p&lt;/i&gt;-Class Tower Groups

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Index-<i>p</i> Abelianization Data of <i>p</i>-Class Tower Groups