Bicyclic commutator quotients with one non-elementary component

Bicyclic commutator quotients with one non-elementary component

For any number field $K$ with non-elementary $3$-class group ${\rm Cl}_3(K)\simeq C_{3^e}\times C_3$, $e\ge2$, the punctured capitulation type $\varkappa(K)$ of $K$ in its unramified cyclic cubic extensions $L_i$, $1\le i\le4$, is an orbit under the action of $S_3\times S_3$. By means of Artin'...

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Bibliographic Details
Main Author: Daniel C. Mayer
Format: Article
Language:English
Published: Institute of Mathematics of the Czech Academy of Science 2023-07-01
Series:Mathematica Bohemica
Subjects:
hilbert $3$-class field tower
maximal unramified pro-$3$ extension
unramified cyclic cubic extensions
galois action
imaginary quadratic fields
bicyclic $3$-class group
punctured capitulation types
statistics
pro-$3$ groups
finite $3$-groups
generator rank
relation rank
schur $\sigma$-groups
low index normal subgroups
kernels of artin transfers
abelian quotient invariants
$p$-group generation algorithm
descendant trees
antitony principle
Online Access:http://mb.math.cas.cz/full/148/2/mb148_2_2.pdf

Internet

http://mb.math.cas.cz/full/148/2/mb148_2_2.pdf

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