### Definition of Abelian

1. n. One of a sect in Africa (4th century), mentioned by St. Augustine, who states that they married, but lived in continence, after the manner, as they pretended, of Abel.

### Definition of Abelian

1. Adjective. (mathematics dated) (alternative capitalization of abelian) ¹

2. Noun. (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. ¹

3. Adjective. (mathematics) Having a commutative defining operation. ¹

¹ Source: wiktionary.com

### Definition of Abelian

1. being a commutative group in mathematics [adj]

### Abelian Pictures

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### Lexicographical Neighbors of Abelian

 abecedariusabecedariusesabecedaryabecediariesabecediaryabecedismabecedismsabedabediterolabegge abeggingabeighabeleabelesabeliaabelian (current term)abelian groupabelian groupsabelianisationabelianization abelianizedabeliannessabeliasabelisaurabelisauridabelisauridsabelisaursabelmoskabelmosksabelmusk

### Literary usage of Abelian

Below you will find example usage of this term as found in modern and/or classical literature:

1. Theory and Applications of Finite Groups by George Abram Miller, Hans Frederick Blichfeldt, Leonard Eugene Dickson (1916)
"A necessary and sufficient condition that a group be abelian is that each ... Find the number of subgroups with invariants 6, 2 in the abelian group whose ..."

2. Algebraic Equations by George Ballard Mathews (1907)
"abelian EQUATIONS. 40. A GROUP is said to be abelian when its elements satisfy the commutative law of multiplication: that is to say when ss' = s's, ..."

3. A Treatise on the Theory of Functions by James Harkness, Frank Morley (1893)
"mentioned below, will be found useful helps to the acquisition of a working knowledge of Riemann's methods. The standard treatise on abelian functions is ..."

4. Encyclopaedia Britannica, a Dictionary of Arts, Sciences, Literature and edited by Hugh Chisholm (1910)
"If S], S.-, Sj S, are the linear substitutions that of an abelian group G and the corresponding factor groups G/H ire abelian, this result follows ..."

5. Engineering Mathematics: A Series of Lectures Delivered at Union College by Charles Proteus Steinmetz (1911)
"They are called abelian integrals and abelian functions. Thus in the most general case (1), the explicit function corresponding to (1) being J/=/Cr), ..."

6. The Geometric Theory of Ordinary Differential Equations and Algebraic Functions by Georges Valiron (1984)
"abelian INTEGRALS 20 - Periods of Abel ian Integrals Let R(z,u) be a rational fraction of s and u. An abelian integral is an integral M 1(M) = fR(z,u) dz ..."

7. Topics in Physical Geometry by Robert Hermann (1988)
"make certain useful general remarks about the structure of the orbits of abelian Lie algebras of vector fields and the isotropy and holonomy structure of ..."

8. Introduction to the Theory of Algebraic Equations by Leonard Eugene Dickson (1903)
"REGULAR CYCLIC EQUATIONS; abelian EQUATIONS. 85. ... A more general type of "abelian equations" was studied by Abel, (Euvres, I, No. XI, pp. 114-140. ..."