profinite group
Word Rarity
Very rare
Frequency: Zipf frequency 0.00 in modern English
22
Scrabble Score
14
Letters
2
Syllables
10
Unique Chars
Meaning
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.
Example Sentences
- "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."
- "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 of a "quasi-free profinite group" (Section 10.6)."
- "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."
Inflected Forms
profinite groups (plural)
pro-finite group (alternative)
Phrases
profinite integer
profinite word