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1. Abelian group: A group whose operation is commutative (cf. Commutativity). (Mathematics) [100%] 2023-09-21
2. Abelian group: In the mathematical field of abstract algebra, an abelian group is a type of group in which the group operation is commutative – abelian groups are also known as commutative groups. Abelian groups are named for the mathematician Niels Henrik Abel ... [100%] 2023-06-11
3. Abelian group: 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 does not depend on the order in which they are written. That is, the ... (Commutative group (mathematics)) [100%] 2024-07-30 [Abelian group theory] [Properties of groups]...
4. Abelian 2-group: In mathematics, an Abelian 2-group is a higher dimensional analogue of an Abelian group, in the sense of higher algebra, which were originally introduced by Alexander Grothendieck while studying abstract structures surrounding Abelian varieties and Picard groups. More concretely ... [81%] 2023-12-19 [Abelian group theory] [Algebraic topology]...
5. Torsion abelian group: In abstract algebra, a torsion abelian group is an abelian group in which every element has finite order. For example, the torsion subgroup of an abelian group is a torsion abelian group. [81%] 2023-12-21 [Abelian group theory]
6. Non-abelian group: 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 at least one pair of elements a and b of G, such that a ∗ b ... (1=Group where ab = ba does not always hold) [81%] 2023-11-11 [Properties of groups]
7. Free Abelian group: A group that is free in the variety of all Abelian groups (see Free algebra). Direct sums (of a finite or an infinite number) of infinite cyclic groups, and only these, are free in the class of Abelian groups. (Mathematics) [81%] 2023-09-22
8. Abelian 2-group: In mathematics, an Abelian 2-group is a higher dimensional analogue of an Abelian group, in the sense of higher algebra, which were originally introduced by Alexander Grothendieck while studying abstract structures surrounding Abelian varieties and Picard groups. More concretely ... [81%] 2023-07-17 [Abelian group theory] [Algebraic topology]...
9. Elementary abelian group: In mathematics, specifically in group theory, an elementary abelian group (or elementary abelian p-group) is an abelian group in which every nontrivial element has order p. The number p must be prime, and the elementary abelian groups are a ... (Commutative group in which all nonzero elements have the same order) [81%] 2022-08-02 [Abelian group theory] [Finite groups]...
10. Free abelian group: 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 associative, commutative, and invertible. (Algebra of formal sums) [81%] 2024-01-14 [Abelian group theory] [Properties of groups]...
11. Meta-Abelian group: metabelian group A solvable group of derived length two, i.e. a group whose commutator subgroup is Abelian. (Mathematics) [81%] 2023-10-18
12. Abelian Lie group: In geometry, an abelian Lie group is a Lie group that is an abelian group. A connected abelian real Lie group is isomorphic to \displaystyle{ \mathbb{R}^k \times (S^1)^h }[/math]. [81%] 2023-07-14 [Abelian group theory] [Geometry]...
13. Group theory: In mathematics, groups often arise as structures representing the set of possible symmetries of some object. We have been intentionally vague about the meaning of the terms symmetry and object. [81%] 2023-06-26
14. Group theory: Group theory is the study of mathematical groups, including their symmetries and permutations. It has applications in science, and has become one of the most active branches in all of mathematics in the 20th century. [81%] 2023-03-13 [Algebra]
15. Group theory: Welcome to Group Theory! Group Theory is a vibrant, wide area of current research in mathematics, computer science and mathematical/theoretical physics. [81%] 2024-01-19 [{{PAGENAME}}]
16. Group theory: In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups ... (Branch of mathematics that studies the properties of groups) [81%] 2024-08-13 [Group theory]
17. Abelin: Abelin is a surname, and may refer to: .mw-parser-output .dmbox{display:flex;align-items:center;clear:both;margin:0.9em 1em;border-top:1px solid #ccc;border-bottom:1px solid #ccc;padding:0.25em 0.35em;font-style ... [71%] 2022-06-27
18. Aelian: Aelian or Aelianus may refer to. [71%] 2023-12-16
19. Abelia: B, 376, 1818 Especies * Ver texto * Lista completa de todos los taxones descritos con las sinonimias[1] Sinonimia * Vesalea M. Martens & Galeotti * Zabelia (Rehder) Makino [editar datos en Wikidata] Abelia es un género de unas 70 especies descritas, de las ... [71%] 2023-05-17
20. Locally compact abelian group: In several mathematical areas, including harmonic analysis, topology, and number theory, locally compact abelian groups are abelian groups which have a particularly convenient topology on them. For example, the group of integers (equipped with the discrete topology), or the real ... (Topological group structure arising in Fourier analysis) [70%] 2023-06-09 [Abelian group theory] [Topological groups]...