# Tagged Questions

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### 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. $without$ $theory!$
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### 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 ...
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### 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 PrÃ¼fer groups.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...