Question

Let H={I,r} in D4. Determine all of the distinct left cosets of H in D4. Then...

Let H={I,r} in D4. Determine all of the distinct left cosets of H in D4. Then determine all of the distinct right cosets of H in D4

D4 = {I, R, R^1, R^2, R^3, , rR, rR^1, rR^2, rR^3, } where R^1 stands for rotated 90 degree and r stands for reflection

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
what are the left cosets of dihedral group D2n and their double cosets (H-H) ? let...
what are the left cosets of dihedral group D2n and their double cosets (H-H) ? let the reflection be their subgroup. if you can write them in more details please
Find the left cosets and the right cosets of the subgroup H of G. Is it...
Find the left cosets and the right cosets of the subgroup H of G. Is it the case that aH = Ha for all a ∈ G? Also find (G : H). a) H = {ι, (1 2)(3 4), (1 3)(2 4), (1 4)(2 3)}, G = A4
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.
Let H=<(2 3)> be the cyclic subgroup of G=S3 generated by the transposition (2 3). Write...
Let H=<(2 3)> be the cyclic subgroup of G=S3 generated by the transposition (2 3). Write (as sets) the right-cosets and left-cosets of H in G
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 H = {1, 4, 7} (i) Show that H is a subgroup of U(9). (ii)...
Let H = {1, 4, 7} (i) Show that H is a subgroup of U(9). (ii) Compute all the cosets of H in U(9)
Suppose n = rs where r and s are distinct primes, and let p be a...
Suppose n = rs where r and s are distinct primes, and let p be a prime. Determine (with proof, of course) the number of irreducible degree n monic polynomials in Fp[x]. (Hint: look at the proof for the number of prime degree polynomials) The notation Fp means the finite field with q elements
1. A zero of a polynomial p(x) ∈ R[x] is an element α ∈ R such...
1. A zero of a polynomial p(x) ∈ R[x] is an element α ∈ R such that p(α) = 0. Prove or disprove: There exists a polynomial p(x) ∈ Z6[x] of degree n with more than n distinct zeros. 2. Consider the subgroup H = {1, 11} of U(20) = {1, 3, 7, 9, 11, 13, 17, 19}. (a) List the (left) cosets of H in U(20) (b) Why is H normal? (c) Write the Cayley table for U(20)/H. (d)...
Let A[1, . . . , n] be an array of n distinct numbers. If i...
Let A[1, . . . , n] be an array of n distinct numbers. If i < j and A[i] > A[j], then the pair (i, j) is called an inversion of A. 1. Which arrays with distinct elements from the set {1, 2, . . . , n} have the smallest and the largest number of inversions and why? State the expressions exactly in terms of n. 2. For any 0 < a < 1/2, construct an array for...
Let H be the set of all polynomials of the form p(t) = at2 where a...
Let H be the set of all polynomials of the form p(t) = at2 where a ∈ R with a ≥ 0. Determine if H is a subspace of P2. Justify your answers.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT