Groups of order 12
It is one of my favorite exercises at the end
of the term when students are stuffed with all those notions of
generators and factor groups and p-groups and lower/upper central series
and different decompositions of Jordan-Hölder and outer automorphisms
and so on.
I just say -- I believe that here you have all graphs of subgroups
for groups of order 12:
[Click on any to see the graph, or see all
But why should you believe me? Please, confirm whether there are
other groups of that order; find out the meaning of all the symbols used
there and verify that one actually has full graphs of the subgroups;
invent alternative methods to represent them (for example, how to avoid
replication of conjugate subgroups?); apply all your theoretical tools to
these small, simple examples.
And when they work on it I have time for a cup of coffee.
In fact, a very long series of cups of coffee.
the same, in