abelian group en · NOUN
Pronunciation
- (Southern-England) audio
- /əˈbil.jən ɡɹup/ (US)
- /əˈbi.li.ən ɡɹup/ (US)
Etymology
Named in honour of Niels Henrik Abel (1802–1829), a Norwegian mathematician.
Meanings
-
A group in which the group operation is commutative.
2000, David Arnold, Abelian Groups and Representations of Finite Partially Ordered Sets, Springer, Softcover reprint of 1st edition, page 74, Chapter 2 is a brief introduction to some fundamental techniques for countable torsion-free abelian groups.
By the end of Chapter 2 we had the full power of the Pontryagin Duality Theorem for compact abelian groups and for discrete abelian groups. Locally compact abelian groups are much closer to compact abelian groups than is apparent at first sight.
2013, Karl H. Hofmann, Sidney A. Morris, The Structure of Compact Groups: A Primer for the Student: A Handbook for the Expert, Walter de Gruyter, page 299:1986, Partially Ordered Abelian Groups with Interpolation, American Mathematical Society, 2010 softcover reprint, page 12, Let G and H be partially ordered abelian groups. A positive homomorphism from G to H is any abelian group homomorphism f:G→H that maps positive elements to positive elements, that is, f(G⁺)⊆H⁺.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| Abelian group | alternative | lexicographic | |
| abelian groups | Number=Plur | lexicographic |
Deriveds
Hypernyms
Hyponyms
cyclic group · free abelian group · torsion subgroup
Synonyms
Translations (32)
de kommutative Gruppe (group in which the group operation is commutative) · cmn 阿貝爾群 /阿贝尔群 (group in which the group operation is commutative) · de abelsche Gruppe (group in which the group operation is commutative) · fr groupe commutatif (group in which the group operation is commutative) · sv kommutativ grupp (group in which the group operation is commutative) · pl grupa przemienna (group in which the group operation is commutative) · pl grupa abelowa (group in which the group operation is commutative) · ro grup comutativ (group in which the group operation is commutative) · ja アーベル群 (group in which the group operation is commutative) · is víxlgrúpa (group in which the group operation is commutative) · et Abeli rühm (group in which the group operation is commutative) · nl Abelse ring (group in which the group operation is commutative) · eo komuta grupo (group in which the group operation is commutative) · nl Abelse groep (group in which the group operation is commutative) · ro grup abelian (group in which the group operation is commutative) · eo abela grupo (group in which the group operation is commutative) · is abelsk grúpa (group in which the group operation is commutative) · is víxlin grúpa (group in which the group operation is commutative) · cs abelovská grupa (group in which the group operation is commutative) · is Abel-grúpa (group in which the group operation is commutative) · sh Abelova grupa (group in which the group operation is commutative) · fr groupe abélien (group in which the group operation is commutative) · el αβελιανή ομάδα (group in which the group operation is commutative) · te ఎబిలియన్ సమూహం (group in which the group operation is commutative) · sv abelsk grupp (group in which the group operation is commutative) · hu Abel-csoport (group in which the group operation is commutative) · ru а́белева гру́ппа (group in which the group operation is commutative) · fi Abelin ryhmä (group in which the group operation is commutative) · es grupo abeliano (group in which the group operation is commutative) · pt grupo abeliano (group in which the group operation is commutative) · it gruppo abeliano (group in which the group operation is commutative) · nb abelsk gruppe (group in which the group operation is commutative)