Question

Suppose G is a group such that G= (Z,+). Provide an example of a PROPER subgroup...

Suppose G is a group such that G= (Z,+). Provide an example of a PROPER subgroup of G (i.e. not the identity and not the group itself).

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
Suppose that H is a proper subgroup of G of index n, and that G is...
Suppose that H is a proper subgroup of G of index n, and that G is a simple group, that is, G has no normal subgroups except G itself and {1}. Show thatG can be embedded in Sn.
3. a) Suppose that H is a proper subgroup of Z that contains 12, 30, and...
3. a) Suppose that H is a proper subgroup of Z that contains 12, 30, and 54. What are the possibilities for what H could be? (HINT: You may use without proof that all subgroups of Z are of the formnZ. We will prove this fact later in the semester.) b) Now, suppose that H is a proper subgroup of Z that contains a and b. What are the possibilities for what H could be?
Let G be a non-trivial finite group, and let H < G be a proper subgroup....
Let G be a non-trivial finite group, and let H < G be a proper subgroup. Let X be the set of conjugates of H, that is, X = {aHa^(−1) : a ∈ G}. Let G act on X by conjugation, i.e., g · (aHa^(−1) ) = (ga)H(ga)^(−1) . Prove that this action of G on X is transitive. Use the previous result to prove that G is not covered by the conjugates of H, i.e., G does not equal...
A subgroup H of a group G is called a normal subgroup if gH=Hg for all...
A subgroup H of a group G is called a normal subgroup if gH=Hg for all g ∈ G. Every Group contains at least two normal subgroups: the subgroup consisting of the identity element only {e}; and the entire group G. If G=S(n) show that A(n) (the subgroup of even permuations) is also a normal subgroup of G.
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|
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...
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 let P be a Sylow p-subgroup of G. Suppose...
Let G be a finite group and let P be a Sylow p-subgroup of G. Suppose H is a normal subgroup of G. Prove that HP/H is a Sylow p-subgroup of G/H and that H ∩ P is a Sylow p-subgroup of H. Hint: Use the Second Isomorphism theorem.
Problem 6: Let K be a proper subgroup of H, and H a proper subgroup of...
Problem 6: Let K be a proper subgroup of H, and H a proper subgroup of G. If |K| = 42 and |G| = 420, what are the possible orders of H?
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!
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT