Question

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)

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
Let H be a subgroup of a group G. Let ∼H and ρH be the equivalence...
Let H be a subgroup of a group G. Let ∼H and ρH be the equivalence relation in G introduced in class given by x∼H y⇐⇒x−1y∈H, xρHy⇐⇒xy−1 ∈H. The equivalence classes are the left and the right cosets of H in G, respectively. Prove that the functionφ: G/∼H →G/ρH given by φ(xH) = Hx−1 is well-defined and bijective. This proves that the number of left and right cosets are equal.
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=<(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
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
prouve that let H normal subgroup of G and (|G:H|,|H|)=1 H hall subgroup then H characterstic...
prouve that let H normal subgroup of G and (|G:H|,|H|)=1 H hall subgroup then H characterstic G
Let G be a finite group, and suppose that H is normal subgroup of G. Show...
Let G be a finite group, and suppose that H is normal subgroup of G. Show that, for every g ∈ G, the order of gH in G/H must divide the order of g in G. What is the order of the coset [4]42 + 〈[6]42〉 in Z42/〈[6]42〉? Find an example to show that the order of gH in G/H does not always determine the order of g in G. That is, find an example of a group G, and...
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 H be a subgroup of the group G. Define a set B by B =...
Let H be a subgroup of the group G. Define a set B by B = {x ∈ G | xax−1 ∈ H for all a ∈ H}. Show that H < B.
Let G be the group Z3 + Z4 and let H = h(1, 2)i be the...
Let G be the group Z3 + Z4 and let H = h(1, 2)i be the cyclic subgroup generated by (1, 2). (a) Find the index [G : H] of H in G. (b) Is H a normal subgroup of G? Justify your answer.
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
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT