Phrase guide

profinite group

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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1

noun

Meaning 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.

Definition source: English Wiktionary via Wiktextract

Topics: category-theory, computing, engineering, mathematics, natural-sciences, physical-sciences, sciences, topology

Examples

  • 2014, David Barnes, Constanze Roitzheim, Rational equivariant rigidity, Christian Ausoni, Kathryn Hess, Brenda Johnson, Wolfgang Lück, Jérôme Scherer, An Alpine Expedition through Algebraic Topology, American Mathematical Society, page 14, Recall that a profinite group is an inverse limit of an inverse system of finite groups, with the p-adic numbers being the canonical example. Any finite group is, of course, profinite, but when we talk of a profinite group we assume that the group is infinite.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

2 source translations are retained for this English entry.

  • French: groupe profini — topological group isomorphic to the inverse limit of an inverse system of discrete finite groups
  • German: proendliche Gruppe — topological group isomorphic to the inverse limit of an inverse system of discrete finite groups