Question

Let F be a field. It is a general fact that a finite subgroup G of...

Let F be a field. It is a general fact that a finite subgroup G of (F^*,X) of the multiplicative group of a field must be cyclic. Give a proof by example in the case when |G| = 100.

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
(Modern Algebra) Show that every finite subgroup of the multiplicative group of a field is cyclical....
(Modern Algebra) Show that every finite subgroup of the multiplicative group of a field is cyclical. (Hint: consider m as the order of the finite subgroup and analyze the roots of the polynomial (x ^ m) - 1 in field F)
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 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 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.
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 H a subgroup of G. Let a be an...
Let G be a finite group and H a subgroup of G. Let a be an element of G and aH = {ah : h is an element of H} be a left coset of H. If B is an element of G as well show that aH and bH contain the same number of elements in G.
Let G be a finite group. There are 2 ways of getting a subgroup of G,...
Let G be a finite group. There are 2 ways of getting a subgroup of G, which are {e} and G. Now, prove the following : If |G|>1 is not prime, then G has a subgroup other than the 2 groups which are mentioned in the above.
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...
For an abelian group G, let tG = {x E G: x has finite order} denote...
For an abelian group G, let tG = {x E G: x has finite order} denote its torsion subgroup. Show that t defines a functor Ab -> Ab if one defines t(f) = f|tG (f restricted on tG) for every homomorphism f. If f is injective, then t(f) is injective. Give an example of a surjective homomorphism f for which t(f) is not surjective.
Let F be a field, and let f (x), g(x) ∈ F [x] be nonzero polynomials....
Let F be a field, and let f (x), g(x) ∈ F [x] be nonzero polynomials. Then it must be the case that deg(f (x)g(x)) = deg(f (x)) + deg(g(x)).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT
Active Questions
  • Estimated incidence of diabetes among adults aged ≥18 years, United States, 2015 Characteristic No. in thousands...
    asked 1 minute ago
  • 3. In what stage of Erikson’s psychosocial theory are you currently in? In what stage are...
    asked 5 minutes ago
  • Discrete Mathematics ***Make sure to give proofs in PARAGRAPH form using COMPLETE sentences. Use correct notation...
    asked 14 minutes ago
  • #31. Sociodemographic differences in lung cancer worry. Hahn (2017) evaluated sociodemographic differences in how people worry...
    asked 17 minutes ago
  • The allowable bearing pressure on a 100-ft thick (below the base of footing Es = 55...
    asked 39 minutes ago
  • Write a one to two page paper: Describe how self-concept, self-understanding, and self-esteem change in adolescence.
    asked 1 hour ago
  • 7.) Your participant is 5’8” and weighs 178 lbs. They completed an exercise bout using arm...
    asked 1 hour ago
  • Assume that the price and the demand are both positive. Use the price-demand equation, x= f(p)=  √(1600-2p^2)...
    asked 2 hours ago
  • aBankruptcy: Moral, Amoral, or Immoral? Is it unethical to avoid paying one’s debts by going into...
    asked 2 hours ago
  • Pick a specific leader facing an issue in the last six months that you can analyze...
    asked 2 hours ago
  • For the past several years, Joanna and her two sisters have taken turns claiming a dependency...
    asked 2 hours ago
  • Assume that you developed an e-commerce site for the purpose of doing business. As a continuation...
    asked 2 hours ago