
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 fourthcentury 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]
Lexicographical Neighbors of Abelian
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. 114140. ..."