Recent content by Juneu436

oh ok, so what I said in my previous post means that a normal subgroup of order 5 exists but not a normal subgroup of order 4. However, both a subgroup of order 4 and 5 do exist?

Yeah, but I have to link A4 subset of S4 with the tetrahedra somehow.

If I can show that the group of rotational symmetries of a tetrahedron is A4 and the full group of symmetries of a tetrahedron is S4, then I can conclude that A4 is a subset of S4. Does this approach satisfy the question?

Page 146 from...

Homework Statement A question from artin 6.2: Two tetrahedra can be inscribed into a cube C, each one using half the vertices. Relate this to the inclusion A4 is a subset of S4. The Attempt at a Solution I can only think that the tetrahedral group is isomorphic to A4, and the cube is...

Yeah it is from artin, but I don't have my text with me. So 20/4=5 so there is a subgroup of order 5, and because 20/5=4 there is a subgroup of order 4? Is this enough? Thanks

I think my answer for the order 4 part might not be enough. Is there a general method for this type of question?

Homework Statement Given a class equation of a group H of 20=1+4+5+5+5, does H have a subgroup of order 5? Of order 4? The Attempt at a Solution Order 5 I can't get, but for order 4 I think I am correct in saying that H does have a subgroup of order 4 because each summand in the class...