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Discrete Group
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Geliefert zwischen Mo., 26.01.2026 und Di., 27.01.2026
Details
In mathematics, a discrete group is a group G equipped with the discrete topology. With this topology G becomes a topological group. A discrete subgroup of a topological group G is a subgroup H whose relative topology is the discrete one. For example, the integers, Z, form a discrete subgroup of the reals, R, but the rational numbers, Q, do not.Any group can be given the discrete topology. Since every map from a discrete space is continuous, the topological homomorphisms between discrete groups are exactly the group homomorphisms between the underlying groups. Hence, there is an isomorphism between the category of groups and the category of discrete groups. Discrete groups can therefore be identified with their underlying groups. With this in mind, the term discrete group theory is used to refer to the study of groups without topological structure, in contradistinction to topological or Lie group theory. It is divided, logically but also technically, into finite group theory, and infinite group theory.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786130708627
- Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
- EAN 9786130708627
- Format Fachbuch
- Titel Discrete Group
- Herausgeber Alphascript Publishing
- Anzahl Seiten 80
- Genre Mathematik
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