Word.ws English Dictionary

profinite group

profinite group noun: a topological group that is isomorphic to the inverse limit of some inverse system of discrete finite groups; equivalently, a topological group that is also a Stone space.

Noun

profinite group (plural profinite groups)

  1. A topological group that is isomorphic to the inverse limit of some inverse system of discrete finite groups; equivalently, a topological group that is also a Stone space.
    • This proposition shows that to have a representation with big image of a profinite group, for example, a Galois group, we need to take a profinite topological ring A as a coefficient ring, like the p-adic integer ring #92;Z#95;p.2000, Haruzo Hida, Modular Forms and Galois Cohomology, Cambridge University Press, page 28
    • We have already pointed out that a profinite group G of an infinite rank m is free of rank m if (and only if) G is projective and every finite split embedding problem for G with a nontrivial kernel has m solutions (Proposition 9.4.7). Dropping the condition on G to be projective leads to the notion...2011, Moshe Jarden, Algebraic Patching, Springer, page 207

Forms of profinite group

pluralprofinite groups
alternative formpro-finite group

Questions about profinite group

What does profinite group mean?
Profinite group means a topological group that is isomorphic to the inverse limit of some inverse system of discrete finite groups; equivalently, a topological group that is also a Stone space.
What part of speech is profinite group?
Profinite group is a noun.
What is the plural of profinite group?
The plural of profinite group is profinite groups.

Words near profinite group in the dictionary

  1. profilometrical
  2. profilometrically
  3. profilometries
  4. profilometry
  5. profinite
  6. profinite group
  7. profinite groups
  8. profisetinidin
  9. profit
  10. profit a prendre
  11. profit and loss

Source and license

Adapted from Wiktionary: profinite group (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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