Question

In the group Z12, let H = 〈6〉 and N = 〈8〉. (a) List the elements...

In the group Z12, let H = 〈6〉 and N = 〈8〉.

(a) List the elements of HN/N.

(b) List the elements of H/(H ∩ N).

(c) Define an ismorphism between HN/N and H/(H ∩ N)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In the group Z12, let H = 〈6〉 and N = 〈8〉. (a) List the elements...
In the group Z12, let H = 〈6〉 and N = 〈8〉. (a) List the elements of HN/N. (b) List the elements of H/(H ∩ N). (c) Define an ismorphism between HN/N and H/(H ∩ N).
a) Let H be a subgroup of a group G satisfying [G ∶ H] = 2....
a) Let H be a subgroup of a group G satisfying [G ∶ H] = 2. If there are elements a, b ∈ G such that ab ∈/ H, then prove that either a ∈ H or b ∈ H. (b) List the left and right cosets of H = {(1), (23)} in S3. Are they the same collection?
Let G be a finite group and H a subgroup of G. Let a be an...
Let G be a finite group and H a subgroup of G. Let a be an element of G and aH = {ah : h is an element of H} be a left coset of H. If B is an element of G as well show that aH and bH contain the same number of elements in G.
Let G be a finite group and let H be a subgroup of order n. Suppose...
Let G be a finite group and let H be a subgroup of order n. Suppose that H is the only subgroup of order n. Show that H is normal in G. Hint: Consider the subgroup aHa-1 of G. Please explain in detail!
let g be a group. let h be a subgroup of g. define a~b. if ab^-1...
let g be a group. let h be a subgroup of g. define a~b. if ab^-1 is in h. prove ~ is an equivalence relation on g
Let H be a subgroup of G, and N be the normalizer of H in G...
Let H be a subgroup of G, and N be the normalizer of H in G and C be the centralizer of H in G. Prove that C is normal in N and the group N/C is isomorphic to a subgroup of Aut(H).
Let N and H be groups, and here for a homomorphism f: H --> Aut(N) =...
Let N and H be groups, and here for a homomorphism f: H --> Aut(N) = group automorphism, let N x_f H be the corresponding semi-direct product. Let g be in Aut(N), and  k  be in Aut(H),  Let C_g: Aut(N) --> Aut(N) be given by conjugation by g.  Now let  z :=  C_g * f * k: H --> Aut(N), where * means composition. Show that there is an isomorphism from Nx_f H to Nx_z H, which takes the natural...
In each part below, a group G and a subgroup H are given. Determine whether H...
In each part below, a group G and a subgroup H are given. Determine whether H is normal in G. If it is, list the elements of the quotient group G/H. (a) G = Z-15 × Z-20 and H = <(10, 17)> (b) G = S-6 and H = A-6 (c) G = S-5 and H = A-4
Let G be an Abelian group and let H be a subgroup of G Define K...
Let G be an Abelian group and let H be a subgroup of G Define K = { g∈ G | g3 ∈ H }. Prove that K is a subgroup of G .
Let H = {(1), (1 2)} < G = S3. List the left cosets of H...
Let H = {(1), (1 2)} < G = S3. List the left cosets of H (without repition and listing the elements of each coset). Explain all work.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT