1
vote
5answers
128 views

can somebody recommend a book in a group theory.

can somebody recommend a book in a group theory. that include just questions and their answers. $without$ $theory!$
2
votes
3answers
68 views

Examples of loops which have two-sided inverses.

Are there any neat examples of non-associative loops such that for each element a in the loop there exists $a^{-1}$ so that $a*a^{-1}=1=a^{-1}*a$. Even cooler would be a commutative loop. Also: are ...
0
votes
1answer
35 views

Reference request for Prüfer groups

It will be very helpful for me if I get a reference(notes/book e.t.c) where I can get details about Prüfer groups.
4
votes
0answers
197 views

Characterization of the First Order Theory of Ordered Abelian Groups via Quantifier Elimination

In the paper "Elimination of Quantifiers in Algebraic Structures" Macintyre, McKenna and van den Dries, proved that every field (ordered field) whose theory admits quantifier elimination in the ...
4
votes
2answers
77 views

Reference Request for The Study of Abelian Groups

So I finished Lang's Algebra and after reading this partial Structure Theorem for abelian torsion groups that are not finitely generated , I've gotten interested in abelian groups, in particular ...
13
votes
2answers
405 views

Status of the classification of non-finitely generated abelian groups.

From the Wikipedia on abelian groups: By contrast, classification of general infinitely-generated abelian groups is far from complete. How far are we from a classification exactly? It seems ...
3
votes
3answers
165 views

Constructing a basis for finite abelian groups

Let $G$ be a finite abelian group, and $g_1, \ldots, g_k$ a set of "linearly independent elements", namely such that $\langle g_1 \rangle \oplus \ldots \oplus\langle g_k \rangle$. I would like to ...
3
votes
1answer
154 views

Linear algebra of finite abelian groups

Let $\phi:G \to H$ be a surjective homomorphism of finite abelian groups, and let $g_1, \ldots, g_n$ be an irredundant set of generators (from now on, a basis) for $G$. be a basis for $G$, meaning a ...
2
votes
1answer
257 views

Group Extensions of Finite Abelian Groups

Given a short exact sequence of finite abelian groups, is it possible to classify what groups can show up in the middle based on the kernel and the cokernel? I'm hoping the answer is much easier (than ...