Question

Suppose n and m are integers. Let H = {sm+tn|s ∈ Z and t ∈ Z}....

Suppose n and m are integers. Let H = {sm+tn|s ∈ Z and t ∈ Z}.
Prove that H is a cyclic subgroup of Z.

......................

Please help with clear steps that H is a cyclic subgroup of Z

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 Z be the integers. (a) Let C1 = {(a, a) | a ∈ Z}. Prove...
Let Z be the integers. (a) Let C1 = {(a, a) | a ∈ Z}. Prove that C1 is a subgroup of Z × Z. (b) Let n ≥ 2 be an integer, and let Cn = {(a, b) | a ≡ b( mod n)}. Prove that Cn is a subgroup of Z × Z. (c) Prove that every proper subgroup of Z × Z that contains C1 has the form Cn for some positive integer n.
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!
suppose (Sn) converges to s and (tn) converges to t. use the definition of convergence of...
suppose (Sn) converges to s and (tn) converges to t. use the definition of convergence of sequences to prove that (sn+tn) converges to s+t.
Find Tn for n=10 and plot Tn with arcsin for n=3,6,10. Let T be the nth...
Find Tn for n=10 and plot Tn with arcsin for n=3,6,10. Let T be the nth degree Maclaurin polynomial of arcsin.
Suppose G and H are groups and ϕ:G -> H is a homomorphism. Let N be...
Suppose G and H are groups and ϕ:G -> H is a homomorphism. Let N be a normal subgroup of G contained in ker(ϕ). Define a mapping ψ: G/N -> H by ψ (aN)= ϕ (a) for all a in G. Prove that ψ is a well-defined homomorphism from G/N to H. Is ψ always an isomorphism? Prove it or give a counterexample
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).
3. Let N denote the nonnegative integers, and Z denote the integers. Define the function g...
3. Let N denote the nonnegative integers, and Z denote the integers. Define the function g : N→Z defined by g(k) = k/2 for even k and g(k) = −(k + 1)/2 for odd k. Prove that g is a bijection. (a) Prove that g is a function. (b) Prove that g is an injection . (c) Prove that g is a surjection.
Suppose : phi :G -H is a group isomorphism . If N is a normal subgroup...
Suppose : phi :G -H is a group isomorphism . If N is a normal subgroup of G then phi(N) is a normal subgroup of H. Prove it is a subgroup and prove it is normal?
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 S = {x ∈ Z : −60 ≤ x ≤ 59}. (a) Which integers are...
Let S = {x ∈ Z : −60 ≤ x ≤ 59}. (a) Which integers are both in S and 6Z? (b) Which integers in S have 1 as the remainder when divided by 6? (c) Which integers in S are also in −1 + 6Z? (d) Which integers satisfy n ≡ 3 mod 6?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT