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An algorithm of Katz and its application to the inverse Galois problem

Title data

Dettweiler, Michael ; Reiter, Stefan:
An algorithm of Katz and its application to the inverse Galois problem.
In: Journal of Symbolic Computation. Vol. 30 (2000) Issue 6 . - pp. 761-798.
ISSN 0747-7171
DOI: https://doi.org/10.1006/jsco.2000.0382

Review:

Official URL: Volltext

Abstract in another language

In this paper we present a new and elementary approach for proving the main results of Katz (1996) using the Jordan–Pochhammer matrices of Takano and Bannai (1976) and Haraoka (1994). We find an explicit version of the middle convolution of Katz (1996) that connects certain tuples of matrices in linear groups. From this, Katz’ existence algorithm for rigid tuples in linear groups can easily be deduced. It can further be shown that the convolution operation on tuples commutes with the braid group action. This yields a new approach in inverse Galois theory for realizing subgroups of linear groups regularly as Galois groups over Q. This approach is then applied to realize numerous series of classical groups regularly as Galois groups over Q. In the Appendix we treat an additive version of the convolution.

Further data

Item Type: Article in a journal
Refereed: Yes
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics IV (Number Theory)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics IV (Number Theory) > Chair Mathematics IV (Number Theorie) - Univ.-Prof. Dr. Michael Dettweiler
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 05 May 2023 07:03
Last Modified: 05 May 2023 07:08
URI: https://eref.uni-bayreuth.de/id/eprint/75228