Recent content by POtment

My post was in response to morphism's post. ================== The most natural one-to-one function that maps Z into N is the one that sends the positive integers to the positive even natural numbers, the negative integers to the odd natural numbers, and 0 to 0. The problem is, this map is...

I ended up getting this problem wrong and I was hoping you could give me another hint on: mapping Z to a suitable proper subset of N, one in which we can do something like the even-odd map again? My teacher won't help me find the answer and I will probably need to understand this for the final.

So the permutations of D5= (1); (12345); (15432); (12)(53)(4); (54)(13)(2); (43)(25)(1); (53);(12);(15)(24)(3); (23)(14)(5) Is this correct? How can I show this is isomorphic to D5?

Homework Statement By considering the vertices of the pentagon, show that D5 is isomorphic to a subgroup of S5. Write all permutations corresponding to the elements of D5 under this isomorphism. The Attempt at a Solution To show isomorphic, need to find a function f: D5->S5, where...

OK, that makes sense. I've completed this problem. Thanks!

I'm having some problems completing the proof that the set of even elements forms a group under D4. I do know that if G is any group of permutations then the set of all even permutations G form a subgroup of G, but I'm not sure how to prove that. Does that seem the like the easiest way to go...

The four even then would be (13)(24), (12)(34), (14)(23), and (1), correct? Is 1 even because it is 0 transpositions?

Homework Statement Consider the group D4 (rigid motions of a square) as a subgroup of S4 by using permutations of vertices. Identify all the even permutations and show that they form a subgroup of D4. The Attempt at a Solution I think I have the permutations of correct. They are...

This one is solved. Thanks for nudging me in the right direction!

(0,0), (3,3)

OK. I understand what you are saying and know how to construct the table to find the elements of order 2. However, I still don't understand what the elements of Z6 are. Is it as obvious as 0,1,2,3,4,5?

We are talking about the additive group of Z6. Can you nudge me in the right direction to find the correct elements?

Homework Statement Let G be an abelian group. Show that the set of all elements of G of order 2 forms a subgroup of G. Find all elements of order 2 in Z6. The Attempt at a Solution The elements of Z6 are 1,4,5. I'm not sure how to find the set of all elements of order 2. Can someone help...

Thanks for responding guys. I'm afraid I've led myself down the wrong path with this class. I gave up learning anything from the teacher and have been teaching myself mostly by looking up answers and learning backwards. I have no book to refer to, so I guess I'll just skip this one. Thank you...

I understand that you aren't trying to be mean, and that's exactly what I am trying to do. A worthless teacher and no book leaves me with few options - I was hoping someone here could help me understand that much and I could probably do the rest on my own. No worries, I'll keep trying on my own.