Recent content by jr16

I would like to ask the same question! haha. I think my professor may have added the problem in as a challenge. The text I have is called A First Course in Abstract Algebra (7th ed.) written by John Fraleigh. It's a well written text and I have, for the most part, found it very helpful. I...

It is my understanding that Z6 is the group formed by {0,1,2,3,4,5} under addition mod 6. For example, 3 + 5 = 2.

Thank you again, your input has been extremely helpful. I am working out of a text right now, as part of my undergrad course in abstract algebra. However, the course I am in now has only covered the very beginning of the material. Factor groups have not been covered and sadly appear much later...

Thank you for your response! I suspected all Abelian groups would share that property. As for part (ii) I have looked it up extensively and read much on the topic, however, I am still struggling to fully understand it. Perhaps I just need to see it worded differently. Is it simply...

Homework Statement Consider the subset H = {0,3} of the group Z6. (i) Prove that H is a normal subgroup of Z6. (ii) Prove that Z6/H is isomorphic to Z3. (Give an explicit isomorphism) Homework Equations In order to be a subgroup H must be closed under +6, have an identity, and have an...

ah OK, let's give this another try then :) Prove: (a*b)2 = e (a * b) * (a * b) = LS a * (b * a) * b = LS a * (a * b) * b = LS (a * a) * (b * b) = LS (e) * (e) = LS e = LS = RS Therefore, H is closed under * Is this correct?

Thank you all again for your great responses! I had a small epiphane over breakfast this morning haha It involves something that A. Bahat just brought up, so maybe I finally have it right this time? Prove: a * b = e (a * b)2 = e2 by squaring both sides (a * b) * (a * b) = e * e a * (b * a) * b...

Thank you, all of this input is very helpful! In my original post I should have made it more clear that * in this case does not represent multiplication but rather any binary operation on G. Therefore, sn = s*s*s...n times and sa * sb = s(a+b) Let me try again: Let a, b be elements of...

g2*g2 = e g2 + 2 = e g4 = e (g2)2 = e Therefore, H is closed under * does this fix the issue?

Homework Statement Let <G, *> be an Abelian group with the identity element, e. Let H = {g ε G| g2 = e}. That is, H is the set of all members of G whose squares are the identity. (i) Prove that H is a subgroup of G. (ii) Was being Abelian a necessary condition? Homework Equations For...

Homework Statement For the following set if it has an upper bound, find two different upper bounds as well as the least upper bound (LUB), justifying your answer. If the set has no upper bound, state this and justify your answer. {x | 1 < x < √(7) and x is irrational} (a proof requires the...

So, I let z be an element of the set Un, where zn = 1. Then, by squaring both sides I get: (zn)2 = 12 z2n = 1 Therefore, z must also be an element of the set U2n. Is this correct?

Hey everyone! I would really appreciate some help with this problem. I have been racking my brain for hours now, and nothing seems to work/convince me. Homework Statement Show that Un \subseteq U2n for every positive integer, n. Homework Equations [1] Un = {z ε ℂ, zn = 1} [2] Un =...