# Tagged Questions

Should be used with the (group-theory) tag. A group $(G,*)$ is said to be abelian if $a*b=b*a$ for all $a,b\in G.$

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### Question about accessibility of category of free abelian groups.

I've read, that the accessibility of the category of all free abelian groups is independent on basic set theory (say ZFC). What is the reason for that? And how can I interpret this result? Does it ...
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### Relating Ext groups of abelian groups and group cohomology

One can define $\mathrm{Ext}$-groups in the category of abelian groups (not $\mathbb{Z}[G]$-modules) and group cohomology in very similar ways. The second, group cohomology, can be computed in the ...
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### Abelian group and number of solutions of $x^n=e$

Let $G$ be an abelian group in which the number of solutions of $x^n=e$ is at most $n$ for every positive integer $n$. Show that $G$ is cyclic. I've shown this nice fact only when $|G|$ is finite. ...
### In the group A/B find the order of the coset (x$_1$+2x$_3$)+B
A is an abelian free group, with the base x$_1$,x$_2$,x$_3$. will be B a sub-group that created with x$_1$+x$_2$+4x$_3$,2x$_1$-x$_2$+2x$_3$. In the group A/B find the order of the coset (x$_1$+2x$_3$...
### If $σ^2$ is the identity map from $G$ to $G$, prove that $G$ is abelian.
Let $G$ be a finite group which possesses an automorphism $σ$ such that $σ(g)=g$ if and only if $g=1$. If $σ^2$ is the identity map from $G$ to $G$, prove that $G$ is abelian. This is what I got ...