Recent content by djxl

Ahh, I get it now. Thanks both of you.

The order of (Z/32Z)* (the multiplicative group of units) is phi(32)=16. So if I can show that all elements have order 8 or lower, I've shown that none of them can be generators. I guess my problem is that I don't see how to do this without resorting to a calculator. I'm not sure what you...

Homework Statement Show that \left( \mathbb{Z}/32\mathbb{Z}\right)^{*} is not a cyclic group. Homework Equations The Attempt at a Solution A little calculator magic has showed that all elements in the group have order 8, but that doesn't seem like a very educational solution :). If...

Thanks for the quick help. I understand the solution now o:).

Homework Statement Let G be a group with order \left| G \right| = 60. Assume that G is simple. Now let H be the set of all elements that can be written as a product of elements of order 5 in G. Show that H is a normal subgroup of G. Then conclude that H = G Homework Equations The...