Question

Suppose that G is a cyclic group, with generator a. Prove that if H is a...

Suppose that G is a cyclic group, with generator a. Prove that if H is a
subgroup of G then H is cyclic.

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
Suppose that G is a group and H={x|xg=gx for all g∈G}. a.) Prove that H is...
Suppose that G is a group and H={x|xg=gx for all g∈G}. a.) Prove that H is a subgroup of G. b.) Prove that H is abelian.
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.
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 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 an Abelian group and H a subgroup of G. Prove that G/H is...
Let G be an Abelian group and H a subgroup of G. Prove that G/H is Abelian.
Let G be a cyclic group; an element g ∈ G is called a generator of...
Let G be a cyclic group; an element g ∈ G is called a generator of G if G<g>. Let φ : G → G be an endomorphism of G, and let g be a generator of G. Show that φ is an automorphism if and only if φ(g) is a generator of G. Use this to find Aut(Z).
Prove that if H,K are two subsets in group G with H is the subset of...
Prove that if H,K are two subsets in group G with H is the subset of K, then CG(K)(the centralizer of K in G) is a subgroup of CG(H)
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
Suppose H is a normal subgroup of G where both H and G/H are solvable groups....
Suppose H is a normal subgroup of G where both H and G/H are solvable groups. Prove that G is then a solvable group as well.
Suppose that a cyclic group G has exactly three subgroups: G itself, e, and a subgroup...
Suppose that a cyclic group G has exactly three subgroups: G itself, e, and a subgroup of order p, where p is a prime greater than 2. Determine |G|
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT