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Community Bot
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Does there exist a Galois extension $L/\mathbb{Q}$ with Galois group $A_4$ (the alternating group on four letters) such that all the decomposition groups are cyclic?

This question is motivated by the answer by Kasper Andersen to my questionmy question. Namely, a desired example (if exists) would permit one to answer in the negative this hard questionthis hard question.

Does there exist a Galois extension $L/\mathbb{Q}$ with Galois group $A_4$ (the alternating group on four letters) such that all the decomposition groups are cyclic?

This question is motivated by the answer by Kasper Andersen to my question. Namely, a desired example (if exists) would permit one to answer in the negative this hard question.

Does there exist a Galois extension $L/\mathbb{Q}$ with Galois group $A_4$ (the alternating group on four letters) such that all the decomposition groups are cyclic?

This question is motivated by the answer by Kasper Andersen to my question. Namely, a desired example (if exists) would permit one to answer in the negative this hard question.

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Mikhail Borovoi
Mikhail Borovoi
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A Galois extension over $\mathbb{Q}$ with Galois group $A_4$ and with cyclic decomposition groups

Does there exist a Galois extension $L/\mathbb{Q}$ with Galois group $A_4$ (the alternating group on four letters) such that all the decomposition groups are cyclic?

This question is motivated by the answer by Kasper Andersen to my question. Namely, a desired example (if exists) would permit one to answer in the negative this hard question.