It is asked to show that sublattices of a lattice form a complete lattice under subset relation( I am not sure if the symbol is of just a relation R) and also to show that the lattice of subgroups of a group is complete. First of all I have a doubt about my question that is it asked to find under any relation R or it is subset relation. Then I need a systematic way to show this. I know the definitions. And what if show the one asked in next question by an example?
2026-03-31 16:14:47.1774973687
Sublattices , lattice of subgroups of a group is complete?
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Hint: A lattice is complete if and only if it is closed under arbitrary meets. What is the meet for subgroups or sublattices?
If you find a familiar description of these meets, it is easy to conclude.