Are there only finitely many number fields with given prime factors of discriminant?

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Let $S subseteq mathbb P$ be a finite set of prime numbers. Is it true that there are only finitely many number fields $K$ such that $p mid Delta_K$ implies $p in S$?







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    What about $mathbb Q(zeta_p^r)$ with $S=p$?
    – Mathmo123
    Aug 28 at 15:42











  • Thanks. I posted a follow up question where I explained how this question here arose: math.stackexchange.com/questions/2898107/…
    – principal-ideal-domain
    Aug 29 at 8:38














up vote
0
down vote

favorite












Let $S subseteq mathbb P$ be a finite set of prime numbers. Is it true that there are only finitely many number fields $K$ such that $p mid Delta_K$ implies $p in S$?







share|cite|improve this question
















  • 3




    What about $mathbb Q(zeta_p^r)$ with $S=p$?
    – Mathmo123
    Aug 28 at 15:42











  • Thanks. I posted a follow up question where I explained how this question here arose: math.stackexchange.com/questions/2898107/…
    – principal-ideal-domain
    Aug 29 at 8:38












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Let $S subseteq mathbb P$ be a finite set of prime numbers. Is it true that there are only finitely many number fields $K$ such that $p mid Delta_K$ implies $p in S$?







share|cite|improve this question












Let $S subseteq mathbb P$ be a finite set of prime numbers. Is it true that there are only finitely many number fields $K$ such that $p mid Delta_K$ implies $p in S$?









share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 28 at 14:26









principal-ideal-domain

2,693521




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  • 3




    What about $mathbb Q(zeta_p^r)$ with $S=p$?
    – Mathmo123
    Aug 28 at 15:42











  • Thanks. I posted a follow up question where I explained how this question here arose: math.stackexchange.com/questions/2898107/…
    – principal-ideal-domain
    Aug 29 at 8:38












  • 3




    What about $mathbb Q(zeta_p^r)$ with $S=p$?
    – Mathmo123
    Aug 28 at 15:42











  • Thanks. I posted a follow up question where I explained how this question here arose: math.stackexchange.com/questions/2898107/…
    – principal-ideal-domain
    Aug 29 at 8:38







3




3




What about $mathbb Q(zeta_p^r)$ with $S=p$?
– Mathmo123
Aug 28 at 15:42





What about $mathbb Q(zeta_p^r)$ with $S=p$?
– Mathmo123
Aug 28 at 15:42













Thanks. I posted a follow up question where I explained how this question here arose: math.stackexchange.com/questions/2898107/…
– principal-ideal-domain
Aug 29 at 8:38




Thanks. I posted a follow up question where I explained how this question here arose: math.stackexchange.com/questions/2898107/…
– principal-ideal-domain
Aug 29 at 8:38















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