✦ LIBER ✦

Subgroups of HolQ8as Galois Groups

✍ Scribed by Arne Ledet

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 317 KB
Volume: 181
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0130

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✦ Synopsis

In this paper, we consider nonsplit Galois theoretical embedding problems with cyclic kernel of prime order p, in the case where the ground field has characteristic / p. It is shown that such an embedding problem can always be reduced to another embedding problem, in which the ground field contains the primitive pth roots of unity, and the group extension is central. The reduction is effective, in the sense that a solution to the reduced embedding problem induces a solution to the original embedding problem and that all solutions to the original embedding problem are induced in this way from solutions to the reduced embedding problem. The simplest case of this reduction is then used to give criteria for the realisability of four subgroups of the holomorph Hol Q , where Q is the quaternion group of 8 8 order 8, including the holomorph itself.

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