Galois groups of unramified extensions over maximal cyclotomic fields

Research Project

Project/Area Number	22540019
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Algebra
Research Institution	Kyoto Institute of Technology
Principal Investigator	ASADA Mamoru 京都工芸繊維大学, 工芸科学研究科, 教授 (30192462)
Project Period (FY)	2010 – 2012
Project Status	Completed (Fiscal Year 2012)
Budget Amount *help	¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000) Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000) Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000) Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords	代数学 / 円分体 / 不分岐拡大体
Research Abstract	Let K be the field obtained by adjoining all roots of unity to the rationals. We have strengthened our previous result on unramified Galois extensions of K having non-solvable Galois groups. The result is as follows. There exists an unramified Galois extension of K having the direct product of countable number of copies of SL2(Zp) as the Galois group, p being any prime greater than 3.

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(4 results)