On Noether's problem for cyclic groups of prime order.
In: Proceedings of the Japan Academy, Series A: Mathematical Sciences, Jg. 91 (2015-03-01), Heft 3, S. 39-44
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Zugriff:
Let k be a field and G be a finite group acting on the rational function field k(xg |g∈G) by k -automorphisms h(xg)=xhg for any g,h∈G. Noether's problem asks whether the invariant field k(G)=k(xg |g∈G)G is rational (i.e. purely transcendental) over k . In 1974, Lenstra gave a necessary and sufficient condition to this problem for abelian groups G . However, even for the cyclic group Cp of prime order p, it is unknown whether there exist infinitely many primes p such that Q(Cp) is rational over Q . Only known 17 primes p for which Q(Cp) is rational over Q are p≤43 and p=61,67,71 . We show that for primes p<20000, Q(Cp) is not (stably) rational over Q except for affirmative 17 primes and undetermined 46 primes. Under the GRH, the generalized Riemann hypothesis, we also confirm that Q(Cp) is not (stably) rational over Q for undetermined 28 primes p out of 46 . [ABSTRACT FROM AUTHOR]
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On Noether's problem for cyclic groups of prime order.
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Autor/in / Beteiligte Person: | HOSHI, Akinari |
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Zeitschrift: | Proceedings of the Japan Academy, Series A: Mathematical Sciences, Jg. 91 (2015-03-01), Heft 3, S. 39-44 |
Veröffentlichung: | 2015 |
Medientyp: | academicJournal |
ISSN: | 0386-2194 (print) |
DOI: | 10.3792/pjaa.91.39 |
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