# Abelian

*See also:*

**abelian**

## Contents

## English[edit]

### Etymology[edit]

### Adjective[edit]

**Abelian** (*not comparable*)

- (mathematics, group theory, dated) Alternative letter-case form of
*abelian***1904**, Florian Cajori*An Introduction to the Modern Theory of Equations*, The MacMillan Company, page 214,**Ex. 2.**Show by §§ 187, 188 that there can be no transitive**Abelian**group of prime degree other than the cyclic group, and that there is no irreducible**Abelian**equation of prime degree other than the cyclic equation.

**1914**, Charles Gustave Paul Kuschke,*The Abelian Equations of the Tenth Degree Irreducible in a Given Domain of Rationality*, University of California Press, page 118,- All irreducible
**Abelian**equations of the tenth order belong to the cyclical group of order ten, […] .

- All irreducible
**2004**, Friedrich Kasch, Adolf Mader,*Rings, Modules, and the Total*, Springer (Birkhäuser), page 101,- In this chapter "group" means torsion free
**Abelian**group. The "bible" of**Abelian**group theory is the two volume work of Fuchs [11].

- In this chapter "group" means torsion free

### Noun[edit]

**Abelian** (*plural* **Abelians**)

- (Roman Catholicism, historical) A member of a sect in fourth-century Africa mentioned by St. Augustine, who states that they married but lived in continence after the manner, as they claimed, of Abel.
**1826**, unnamed translator, Pierre Bayle,*An Historical and Critical Dictionary*[1697,*Dictionnaire Historique et Critique*; 1709,*Historical and Critical Dictionary*], Selected and Abridged, Volume 1, page 50,- The
**Abelians**were only a moderate sort of Encratites and Novatians, who absolutely condemned matrimony, while the**Abelians**approved of and retained it.

- The
**1833**, James Flamank,*A Treatise on Happiness*, page 222,- A difference of opinion existed as to the moral effects of matrimony among the early Christians; the
**Abelians**, for instance, suffered no member of their sect to remain single, while the Novatians condemned marriage under every circumstance.

- A difference of opinion existed as to the moral effects of matrimony among the early Christians; the
**1951**, Reginald Reynolds,*Beds: with many noteworthy instances of lying on, under, or about them*, Doubleday, page 256,- If we include heretical sects there is perhaps some similarity to be traced between the syneisaktism of certain Catholic enthusiasts and the customs of the
**Abelians**or Abelonians, who took their name from Abel.

- If we include heretical sects there is perhaps some similarity to be traced between the syneisaktism of certain Catholic enthusiasts and the customs of the

#### Synonyms[edit]

#### Translations[edit]

member of a sect living like Abel