Question

prove that if G is a cyclic group of order n, then for all a in...

prove that if G is a cyclic group of order n, then for all a in G, a^n=e.

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
2.6.22. Let G be a cyclic group of order n. Let m ≤ n be a...
2.6.22. Let G be a cyclic group of order n. Let m ≤ n be a positive integer. How many subgroups of order m does G have? Prove your assertion.
If n is a square-free integer, prove that an abelian group of order n is cyclic.
If n is a square-free integer, prove that an abelian group of order n is cyclic.
Let G be a group of order 4. Prove that either G is cyclic or it...
Let G be a group of order 4. Prove that either G is cyclic or it is isomorphic to the Klein 4-group V4 = {1,(12)(34),(13)(24),(14)(23)}.
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.
Let G be a group of order n and a in G such that a^n =...
Let G be a group of order n and a in G such that a^n = e. Prove or disprove: G = <a>
Let G = <a> be a cyclic group of order 12. Describe explicitly all elements of...
Let G = <a> be a cyclic group of order 12. Describe explicitly all elements of Aut(G), the group of automorphisms of G. Indicate how you know that these are elements of Aut(G) and that these are the only elements of Aut(G).
prove that a factor group of a cyclic group is cyclic. provide explanations.
prove that a factor group of a cyclic group is cyclic. provide explanations.
(abstract alg) Let G be a cyclic group with more than two elements: a) Prove that...
(abstract alg) Let G be a cyclic group with more than two elements: a) Prove that G has at least two different generators. b) If G is finite, prove that G has an even number of generators
Let n be a positive integer. Show that every abelian group of order n is cyclic...
Let n be a positive integer. Show that every abelian group of order n is cyclic if and only if n is not divisible by the square of any prime.
Let a be an element of order n in a group and d = gcd(n,k) where...
Let a be an element of order n in a group and d = gcd(n,k) where k is a positive integer. a) Prove that <a^k> = <a^d> b) Prove that |a^k| = n/d c) Use the parts you proved above to find all the cyclic subgroups and their orders when |a| = 100.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT