Recent content by eddyski3

I have two questions about this group that I think I have an idea about but am unsure of. The first question is how many elements in the Sn group can map 1 to any particular elements, say n-2? The second question is how do you find the order of the stabilizer of 5 in Sn?

Can you explain this further Ben? The way I see it, since G is finite, when you add two elements of H the result might not be in H.

How does the element 1 have finite order in the group you described Bacle?

Yes, as in having an infinite number of elements. What if we wanted a group with order infinity that had a relatively small number of elements of finite order?

Can anyone think of an example of an infinite group that has elements with a finite order?

Oh, ok. Now I understand the argument. Thank you.

I'm not sure how this helps us show that (ba)^2=e? When generalizing to (ab)^n I see we'll get a similar result but I'm not sure how this shows that (ba)^n=e.

Homework Statement If a and b are in a group, show that if (ab)^n=e then (ba)^n=e. Homework Equations The Attempt at a Solution I'm not sure how one would prove this. The question is obviously for non-abelian groups.