✦ LIBER ✦
Division Algebras with PSL(2, q)-Galois Maximal Subfields
✍ Scribed by Elizabeth S Allman; Murray M Schacher
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 104 KB
- Volume
- 240
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
If G is a finite group and k is a field, then G is k-admissible if there exists a G-Galois extension Lrk such that L is a maximal subfield of a k-division algebra.
Ž . We prove that PSL 2, 7 is k-admissible for any number field which either fails to ' contain y1 or which has two primes lying over the dyadic prime. In addition, Ž . PSL 2, 11 is shown to be admissible over ޑ or any number field k with at least two extensions of the dyadic prime. Indeed, there exist infinitely many linearly disjoint admissible extensions for these groups.