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In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named...

In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements...

fundamental theorem of finitely generated abelian groups can be stated two ways, generalizing the two forms of the fundamental theorem of finite abelian groups...

In mathematics, the Mordell–Weil theorem states that for an abelian variety A {\displaystyle A} over a number field K {\displaystyle K} , the group A (...

numbers. By invoking the Kodaira embedding theorem and Chow's theorem one may equivalently define a complex abelian variety of dimension g to be a complex...

theorem with the use of strong induction and the class equation, though considerably less machinery is required to prove the theorem in the abelian case...

{L} )} . Abelian theorem: If a series is convergent to A {\displaystyle A} then it is Lambert summable to A {\displaystyle A} . Tauberian theorem: Suppose...

of divergent series, and their summation methods, contains many theorems of abelian type and of tauberian type. Abel's summation formula – Integration...

are all abelian. The order of GL2(Fq) is (q2 − 1)(q2 − q) = (q)(q + 1)(q − 1)2. Since q = pnm + 1, the order of GL2(Fq) = p2n m′. Thus by Theorem 1, the...

In mathematics, a free abelian group is an abelian group with a basis. Being an abelian group means that it is a set with an addition operation that is...

finitely generated abelian group. (This is Mordell's Theorem, later generalized to the Mordell–Weil theorem.) Moreover, Mazur's torsion theorem restricts the...

In mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (G, ∗) in which there exists...

In mathematics, the Torelli theorem, named after Ruggiero Torelli, is a classical result of algebraic geometry over the complex number field, stating...

addition theorems can be said to hold. A more modern aspect is the theory of formal groups. Timeline of abelian varieties Addition theorem for spherical...

Mitchell's embedding theorem, also known as the Freyd–Mitchell theorem or the full embedding theorem, is a result about abelian categories; it essentially...

each non-Abelian finite simple group has order divisible by at least three distinct primes. The Feit–Thompson theorem, or odd order theorem, states that...

The motivating prototypical example of an abelian category is the category of abelian groups, Ab. Abelian categories are very stable categories; for...

specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship between quotients...

for the CN-theorem and the odd order theorem. The proof can be broken up into three steps. We let G be a non-abelian (minimal) simple group of odd order...

compact sets. The Pontryagin duality theorem establishes Pontryagin duality by stating that any locally compact abelian group is naturally isomorphic with...