Cyclic Reduction of Central Embedding Problems

✍ Scribed by H. Opolka

• Book ID: 102568779
• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 152 KB
• Volume: 159
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1993.1160

✦ Synopsis

It is shown that every central embedding problem (E) for the absolute Galois group (\mathscr{G}) of a number field has a so-called cyclic reduction (E^{\prime}); this is a central embedding problem for (\mathscr{G}) with a cyclic quotient group (J) of (\mathscr{G}) such that (E) is solvable if and only if (E^{\prime}) is solvable. Some information about the minimal order of (J) is also provided. (C 1993) Academic Press, Inc.