Question

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.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let G be a finitely generated group, and let H be normal subgroup of G. Prove...
Let G be a finitely generated group, and let H be normal subgroup of G. Prove that G/H is finitely generated
1) Let G be a group and N be a normal subgroup. Show that if G...
1) Let G be a group and N be a normal subgroup. Show that if G is cyclic, then G/N is cyclic. Is the converse true? 2) What are the zero divisors of Z6?
Let G be a group and suppose H = {g5 : g ∈ G} is a...
Let G be a group and suppose H = {g5 : g ∈ G} is a subgroup of G. (a) Prove that H is normal subgroup of G. (b) Prove that every element in G/H has order at most 5.
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 G be a finite group and H be a subgroup of G. Prove that if...
Let G be a finite group and H be a subgroup of G. Prove that if H is only subgroup of G of size |H|, then H is normal 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 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...
f H and K are subgroups of a group G, let (H,K) be the subgroup of...
f H and K are subgroups of a group G, let (H,K) be the subgroup of G generated by the elements {hkh−1k−1∣h∈H, k∈K}. Show that : H◃G if and only if (H,G)<H
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
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT