In: Advanced Math
For a tetrahedron
-describe the type of groups of a rectangle
-describe the orders of the groups
-describe the structure of the groups
-describe the elements of the groups (make sure to name all the elements and describe them as a group of permutations on the vertices)
- describe each group as subgroups of permutation groups
-describe all possible orders, types and generators for each subgroup of the group
-are any of these groups cyclic and or abelian?
-are any of these subgroups cyclic and or abelian?
-are there subgroups of every possible order?
-which subgroups are isomorphic and how do you know?