There are no entire elliptic functions except the constants (Liouville's theorem).
are integers (a special case of Abel's theorem, see [[Abelian function|Abelian function]]).
9 KB (1,292 words) - 19:08, 20 January 2022
...ediaofmath.org/legacyimages/b/b015/b015310/b01531041.png" /> is a sheaf of
Abelian groups, then for every <img align="absmiddle" border="0" src="https://www.e
...hemes — see [[#References|[2]]] — can also be interpreted as a base-change
theorem); or 3) <img align="absmiddle" border="0" src="https://www.encyclopediaofma
11 KB (1,513 words) - 17:08, 7 February 2011
[[Abelian variety|Abelian variety]] (cf. also
[[Abelian differential|Abelian differential]]). The polarization class
10 KB (1,582 words) - 22:02, 5 March 2012
...belian varieties and behaves as a functor with respect to the morphisms of Abelian varieties preserving the zero point. For the local aspect see [[#References
...ess (1974) (Appendix in Russian translation: Yu.I. Manin; The Mordell–Weil theorem (in Russian)) {{MR|2514037}} {{MR|1083353}} {{MR|0352106}} {{MR|0441983}} {
6 KB (893 words) - 08:43, 1 May 2023
...gory|Topologized category]]) in dimensions 0, 1. A unified approach to non-Abelian cohomology can be based on the following concept. Let $ C ^{0} $,
fixed. Then a non-Abelian cochain complex is a collection $$
12 KB (1,712 words) - 09:30, 20 December 2019
...maximum condition for subgroups is equivalent to the maximum condition for Abelian subgroups [[#References|[4]]]. A similar result was also established for th
...ups and locally nilpotent groups. It was found, in particular, that if all Abelian subgroups of a locally nilpotent torsion-free group (cf. [[Group without to
5 KB (720 words) - 17:15, 7 February 2011
...y existence condition. A non-trivial restriction is the Bruck–Ryser–Chowla theorem, see [[Block design|Block design]]. This condition is not sufficient, as th
...method for symmetric designs which combines Abelian difference sets (cf. [[Abelian difference set]]; [[Difference set|Difference set]]; [[Difference set|Diffe
7 KB (1,152 words) - 16:45, 1 July 2020
A nilpotent, in particular an Abelian, Lie group is solvable. If $ F = \{ V _{i} \} $ is a complete [[Flag|fla
An analogue of Lie's theorem on solvable Lie algebras is true for solvable Lie groups: If $ \rho : \
7 KB (1,043 words) - 18:17, 12 December 2019
...between [[topological group]]s and their [[character group]]s. The duality theorem states that if $ G $
is a locally compact Abelian group and if $ X ( G) $
10 KB (1,483 words) - 17:06, 13 June 2020
$#C+1 = 70 : ~/encyclopedia/old_files/data/L058/L.0508000 Lefschetz theorem
Lefschetz' fixed-point theorem, or the Lefschetz–Hopf theorem, is a theorem that makes it possible to express the number of fixed points of a continuou
11 KB (1,584 words) - 11:51, 8 April 2023
$#C+1 = 261 : ~/encyclopedia/old_files/data/A110/A.1100040 Abelian surface
An [[Abelian variety|Abelian variety]] of dimension two, i.e. a complete connected group variety of dime
18 KB (2,511 words) - 06:25, 26 March 2023
and an Abelian group $ G $.
see [[De Rham theorem|de Rham theorem]]).
16 KB (2,386 words) - 16:47, 20 January 2024
...lpotent as an abstract group (cf. [[Nilpotent group|Nilpotent group]]). An Abelian Lie group is nilpotent. If $ F = \{ V _{i} \} $ is a [[Flag|flag]] in a
...p version of Engel's theorem admits the following strengthening (Kolchin's theorem): If $ G $ is a subgroup of $ \mathop{\rm GL}\nolimits (V) $ , where
5 KB (803 words) - 18:12, 12 December 2019
The Mittag-Leffler theorem on expansion of a meromorphic function (see , ) is one of the basic theorem
The Mittag-Leffler theorem implies that any given meromorphic function $f(z)$ in $\mathbb{C}$ with pol
6 KB (980 words) - 18:47, 24 May 2017
...also [[Graph automorphism|Graph automorphism]]). This is know as Frucht's theorem. In 1949, Frucht [[#References|[a3]]] extended this result by showing that
...ese results see [[#References|[a4]]]. For an alternative proof of Frucht's theorem see [[#References|[a5]]].
3 KB (387 words) - 09:29, 19 January 2021
...oduct|Direct product]]) of $R$-groups, are $R$-groups. The following local theorem is valid for the class of $R$-groups: If all finitely-generated subgroups o
1 KB (254 words) - 11:47, 29 June 2014
Theorem 1) was later strengthened; namely, it was proved that the condition $ a _
...should mean. In [[#References|[a1]]], p. 195, is written: " a theorem is Abelian if it says something about an average of a sequence from a hypothesis about
11 KB (1,603 words) - 10:19, 7 May 2021
...athbf{Z}$, then this is true only under the condition that $L/M$ is a free Abelian group [[#References|[2]]]. The finitely-generated subalgebras of a free Lie
...belong to $L(X)$ are given by the Specht–Wever theorem and the Friedrichs theorem, respectively. The first one says that a homogeneous element $a$ of degree
3 KB (564 words) - 19:53, 15 March 2023
...uction associated with special radical subcategories; it first appeared in Abelian categories in the description of the so-called Grothendieck categories in t
be an [[Abelian category|Abelian category]]. A full subcategory $ {\mathfrak A ^ \prime } $
10 KB (1,375 words) - 22:17, 5 June 2020
...n a number of areas of analysis. If $\{x_k\}$ is a sequence in a Hausdorff Abelian [[Topological group|topological group]] $(G,\tau)$, then $\{x_k\}$ is $\tau
...rem|Banach–Steinhaus theorem]] and the [[Mazur–Orlicz theorem|Mazur–Orlicz theorem]] on the joint continuity of separately continuous bilinear operators are p
3 KB (545 words) - 12:08, 3 August 2014