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Martin Brandenburg
Martin Brandenburg
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Is every profinite group a Galois group?spaces coming from profinite groups

This is probably well-known:

  • Does every nonempty profinite space occur as the underlying space of a profinite group? If not, which conditions have to be imposed?

  • Is every profinite group isomorphic to the Galois group of some Galois extension?

Does every nonempty profinite space occur as the underlying space of a profinite group? If not, which conditions have to be imposed?

- Is every profinite group isomorphic to the Galois group of some Galois extension? (yes, see the comments)

Is every profinite group a Galois group?

This is probably well-known:

  • Does every nonempty profinite space occur as the underlying space of a profinite group? If not, which conditions have to be imposed?

  • Is every profinite group isomorphic to the Galois group of some Galois extension?

profinite spaces coming from profinite groups

This is probably well-known:

Does every nonempty profinite space occur as the underlying space of a profinite group? If not, which conditions have to be imposed?

- Is every profinite group isomorphic to the Galois group of some Galois extension? (yes, see the comments)

Source Link
Martin Brandenburg
Martin Brandenburg
  • 63.1k
  • 13
  • 207
  • 424

Is every profinite group a Galois group?

This is probably well-known:

  • Does every nonempty profinite space occur as the underlying space of a profinite group? If not, which conditions have to be imposed?

  • Is every profinite group isomorphic to the Galois group of some Galois extension?