Example 4.2: Lets find all the subgroups of the given group and draw the lattice diagram for the subgroup.
- Z12
- Z36
- Z8
In the book finding the subgroups is explained well but it does not explain how the lattice diagram is form. What is lattice diagram by the way in abstract algebra? Lattice diagram I know is from multiplication in grade school and some review in high school and history in math course (MATH 023) but not this kind. Can someone please explain why it is formed like that (with trees and ect.)? Probably many will laugh with this question but I am new to this kind of topic.
The book probably means the Hasse diagram of the lattice of subgroups of a given group.
In this context, lattice is special type of partially ordered set. The partial order here is set inclusion.