https://**en.wikipedia.org**/wiki/**Rank_of_an_abelian_group**

Definition. A subset {a α} of an abelian group is linearly independent (over Z) if the only linear combination of these elements that is equal to zero is trivial: if

https://**en.wikipedia.org**/wiki/**Rank_of_a_group**

For the dimension of the Cartan subgroup, see Rank of a Lie group. In the mathematical subject of group theory, the **rank of a group** G, denoted rank(G), can refer to ...

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Learn and talk about **Rank of an abelian group** , and check out Rank of an abelian ...

math.stackexchange.com/questions/1311852/**rank-of-an-abelian-group**

I learned that a **rank of an abelian group** is defined by a cardinality of maximal linearly independent sets. But how we can say that this is well-defined?

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**Rank of an abelian group** is analogous to the dimension of a vector space. The main difference with the case of vector space is a presence of torsion.

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In mathematics, the rank, Prüfer rank, or torsion-free **rank of an abelian group** A is the cardinality of a maximal linearly independent subset.

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In mathematics, the rank, or torsion-free **rank, of an abelian group** measures how large a group is in terms of how large a vector space one would need to "contain" it ...

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Definitions of **Rank of an abelian group**, synonyms, antonyms, derivatives of **Rank of an abelian group**, analogical dictionary of **Rank of an abelian group** (English)