Solution Found!

Suppose that G is an Abelian group of order 35 and every

Chapter 4, Problem 20E

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Problem 20E

Suppose that G is an Abelian group of order 35 and every element of G satisfies the equation x35 = e. Prove that G is cyclic. Does your argument work if 35 is replaced with 33?

Questions & Answers

QUESTION:

Problem 20E

Suppose that G is an Abelian group of order 35 and every element of G satisfies the equation x35 = e. Prove that G is cyclic. Does your argument work if 35 is replaced with 33?

ANSWER:

Step 1 of 5

As  is an abelian group order 35, the order of element will be,

                                                     

For element  with order 5 and element  with order 7,

                                                   

From the above result, order of  divides the value 35. Then, the order of  can be,

                                                    

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back