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toward the end: "Theorem: Let F be a free abelian group generated by the set and let be a subgroup. Then G is free." Ordinarily the terminology used would...

The comment(s) below were originally left at Talk:Abelian group/Comments, and are posted here for posterity. Following several discussions in past years...

I added some sources for the definition of free abelian groups; however the definition of abelian groups themselves is still unsourced. —David Eppstein...

that a free abelian group is not the same as an abelian free group is that in an free group ab ≠ ba, necessarily, but in an abelian free group, a+b=b+a...

in reference to Wikipedia's rules on capitalisation and the page on abelian groups SetaLyas (talk) 10:01, 16 April 2008 (UTC) Actually, the title really...

Currently, torsion-free abelian group redirects here, but I think its supposed to have its own article. See e.g. Torsion-free abelian groups of rank 1. The...

upper-case first letter. Is there any reason why, instead of "Abelian", mostly "abelian" is being used? S. — Preceding unsigned comment added by 217.168...

full-text PDF file freely downloadable) says Łoś calls a torsion-free abelian group A slender if every homomorphism of P into A sends all but a finite...

description of a group whether it is free? --Radu Raduberinde (talk) 2008-07-16T21:01:54 This is more a question of logic, than of abelian groups. I think perhaps...

who use abelian categories, and who need to prove that a given category is an abelian category, know that definition. The definition of abelian category...

statement "every lattice in C n {\displaystyle \mathbb {C} ^{n}} is a free abelian group of rank 2n." I guess the rank should be n. Sanpitch (talk) 19:23,...

(UTC) something about p-ranks? (rank r ( A ) {\displaystyle r(A)} of an abelian group A {\displaystyle A} is the non-torsion rank r 0 ( A ) {\displaystyle...

Néron model for the abelian variety over the Dedekind domain (meaning that the generic point of the model is the original abelian variety over the number...

numbers forms a group. However, both the group G and the abelian group G/[G,G], define the same group of homomorphisms, so there is no generality gained in...

terminology is tricky because abelian scheme is a concept derived from abelian variety, and therefore it is usual to say "commutative group scheme". Charles Matthews...

semimodule is just like a module, except that the underlying abelian group is replaced with an abelian semigroup, so the elements do not necessarily have inverses...

all group algebras are commutative if G is abelian (with the converse being true in the non-pathological cases), and for finite groups, all group algebras...

defines "lattice" as a free abelian group of finite rank possessing an integral symmetric bilinear form. The article lattice (group), on the other hand,...

a free abelian group of rank two is a Baumslag-Solitar group (Baumslag–Solitar group's presentation makes it clear B(1,1) is such), and that a group containing...

someone with no account: as I write (18th Nov 09) it says, in the non-abelian cohomology section: "The first cohomology of G with coefficents in A is...