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Results tagged with abelian-groups
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user 5513
For questions about groups whose elements commute.
24
votes
The existence of non-trivial homomorphisms $\prod_{n=1}^{\infty}\mathbb{Z}/\bigoplus_{n=1}^{...
Here's an elementary proof that doesn't require ultrafilters, but uses axiom of choice.
The group
\begin{equation*}
\prod_{n=1}^\infty \mathbb{Z} / \bigoplus_{n=1}^\infty \mathbb{Z}
\end{equation*}
…
- 4,790
1
vote
Accepted
Example involving partially ordered Abelian groups
Let $G=\mathbb{R}^2$ with order defined by
$(a_1,a_2)\leq (b_1,b_2) \iff a_1\leq b_1$ and $a_2\leq b_2$.
Let $u=(1,1)$ and let $g_0=(1,2)$.
Then $p(g_0)=1$ and $r(g_0)=2$.
- 4,790