BICYCLIC COMMUTATOR QUOTIENTS WITH ONE NON-ELEMENTARY COMPONENT

被引：1

作者：

Mayer, Daniel C. ^{[1
]}

机构：

[1] Naglergasse 53, A-8010 Graz, Austria

来源：

MATHEMATICA BOHEMICA | 2023年 / 148卷 / 02期

基金：

奥地利科学基金会;

关键词：

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 s-groups; low index normal subgroups; kernels of Artin transfers; abelian; quotient invariants; p-group generation algorithm; descendant trees; antitony principle; CLASS FIELDS; TOWERS;

D O I：

10.21136/MB.2022.0127-21

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For any number field K with non-elementary 3-class group Cl-3(K).(sic) C-3(e) xC(3), e greater than or less than 2, the punctured capitulation type n(K) of K in its unramified cyclic cubic extensions Li, 1i 1 less than or greater than 1 less than or greater than 4, is an orbit under the action of S3 xS3. By means of Artin's reciprocity law, the arithmetical invariant n(K) is translated to the punctured transfer kernel type {(G2) of the automorphism group G2 = Gal(F2 3 (K)/K) of the second Hilbert 3-class field of K. A classification of finite 3-groups G with low order and bicyclic commutator quotient G/G'. C3e x C3, 2 6 e 6 6, according to the algebraic invariant n(G), admits conclusions concerning the length of the Hilbert 3-class field tower F-infinity (3) (K) of imaginary quadratic number fields K.

引用

页码：149 / 180

页数：32