# Thread: group theory, Orbits of a cube

1. ## group theory, Orbits of a cube

I have been trying to work through some group theory questions but have no idea how to solve the ones iv been given. The question is for a tutorial but it is not assessed so I would appreciate any help i can get with it so i can ask my tutor better questions than were do i even start. Hopefully I should be able to solve the other questions on my own with the help i receive on this.

Question
Fix a line L through opposite vertices of a cube. Consider the subgroup H of
the symmetries of the cube generated by g, where g is a rotation by 1/3 of a turn
about L. Then H acts on the set of vertices of the cube. Describe the orbits.

Thanks Caitlin

2. Originally Posted by CHAYNES
I have been trying to work through some group theory questions but have no idea how to solve the ones iv been given. The question is for a tutorial but it is not assessed so I would appreciate any help i can get with it so i can ask my tutor better questions than were do i even start. Hopefully I should be able to solve the other questions on my own with the help i receive on this.

Question
Fix a line L through opposite vertices of a cube. Consider the subgroup H of
the symmetries of the cube generated by g, where g is a rotation by 1/3 of a turn
about L. Then H acts on the set of vertices of the cube. Describe the orbits.

Thanks Caitlin
It is 120-degree rotations about line L through opposite vertices of a cube. Thus, the order of H is 3. Try first a vertex in a cube and see how it rotates by the action of H. The stabilizer of a vertex that L intersects is H itself.