论文标题
有限的非密西比里舒尔sigma-galois集体塔塔
Finite non-metabelian Schur sigma-Galois groups of class field towers
论文作者
论文摘要
对于每个奇数prime p> = 5，存在有限的p组G，具有派生的商g/d（g）= c（p）xc（p）（p）和几乎恒定的传输内核型k（g）=（1,2，...，...，2）具有两个固定点。事实证明，对于P = 7，这种类型的K（g）具有最简单的对数亚洲商不变的情况，t（g）=（g）=（11111,111,11,21,21,21,21,21,21,21,21,21）在八个最大亚组中，由98个非米特布尔式SCMMA-SCMMA-SCMAMMMA-GROFF（SIGMMA-SCMMA-GROVEN）完全实现。和7^7阶的Metabelianizations s/d（d（s））。对于P = 5，具有T（G）的K型=（2111,11,11,11,21,21,21,21,21）导致无限的许多非金属盐Schur Sigma-groups sord sord sord s sord s sord s Order sord s Order sord s of 5^14至少无绑定的衍生长度DL（s）> = 3和Metabelianizations s/d（S/D（d（S/d））。这些结果承认了以下结论：d = -159592是一个假想二次式磁场的首个已知判别，具有7级的田野塔，具有精确的长度为l = 3，d = -90868是对假想的二次二等磁场的判别，其长度为5级field tower l> = 3，其长度仍然是未知的。
For each odd prime p>=5, there exist finite p-groups G with derived quotient G/D(G)=C(p)xC(p) and nearly constant transfer kernel type k(G)=(1,2,...,2) having two fixed points. It is proved that, for p=7, this type k(G) with the simplest possible case of logarithmic abelian quotient invariants t(G)=(11111,111,21,21,21,21,21,21) of the eight maximal subgroups is realized by exactly 98 non-metabelian Schur sigma-groups S of order 7^11 with fixed derived length dl(S)=3 and metabelianizations S/D(D(S)) of order 7^7. For p=5, the type k(G) with t(G)=(2111,111,21,21,21,21) leads to infinitely many non-metabelian Schur sigma-groups S of order at least 5^14 with unbounded derived length dl(S)>=3 and metabelianizations S/D(D(S)) of fixed order 5^7. These results admit the conclusion that d=-159592 is the first known discriminant of an imaginary quadratic field with 7-class field tower of precise length L=3, and d=-90868 is a discriminant of an imaginary quadratic field with 5-class field tower of length L>=3, whose exact length remains unknown.
