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...
36 KB (5,284 words) - 20:43, 1 August 2024
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...
49 KB (6,756 words) - 01:09, 13 November 2023
In abstract algebra, an abelian group ( G , + ) {\displaystyle (G,+)} is called finitely generated if there exist finitely many elements x 1 , … , x s...
12 KB (1,658 words) - 07:13, 19 May 2024
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...
2 KB (216 words) - 16:58, 13 July 2024
algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by...
21 KB (2,918 words) - 10:20, 25 April 2024
an abelian group A is the cardinality of a maximal linearly independent subset. The rank of A determines the size of the largest free abelian group contained...
7 KB (1,132 words) - 22:35, 10 December 2022
In mathematics, specifically in group theory, an elementary abelian group is an abelian group in which all elements other than the identity have the same...
8 KB (991 words) - 01:17, 29 June 2024
topological abelian group, or TAG, is a topological group that is also an abelian group. That is, a TAG is both a group and a topological space, the group operations...
2 KB (301 words) - 12:22, 13 August 2023
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...
459 bytes (48 words) - 08:28, 4 August 2020
notion is a free abelian group; both notions are particular instances of a free object from universal algebra. As such, free groups are defined by their...
18 KB (2,309 words) - 19:40, 25 May 2024