(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How do the atoms and coatoms of the lattice of all subgroups of the group [itex]\mathbb{Z}(+,-,0)[/itex] look like?

2. Relevant equations

Let [itex](L,\le)[/itex] be a lattice and [itex]e, f \in L[/itex] is the minimum (maximum) elements of L. Then we say that [itex]a, b \in L[/itex] is the atom (coatom) of L ifacoverse(bcoversf).

3. The attempt at a solution

I guess that all subgroups of the given group are of form [itex]H = k\mathbb{Z} = \left\{ k.x | x \in \mathbb{Z}\right\}[/itex] and that the ordering on the lattice will be set inclusion.

But I don't know how its Hasse diagram will look like (I think I need it to solve the problem).

Thank you for any hint!

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# Lattice of subgroups

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