Solution Found!

Suppose the and are isomorphisms of some group G to the

Chapter 6, Problem 49E

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Suppose the ? and ? are isomorphisms of some group G to the same group. Prove that H = {g? G | ?(g) = ?(g)} is a subgroup of G.

Questions & Answers

QUESTION:

Suppose the ? and ? are isomorphisms of some group G to the same group. Prove that H = {g? G | ?(g) = ?(g)} is a subgroup of G.

ANSWER:

Step 1 of 2

Suppose the and are isomorphisms from some group to the same group.

To prove that is a subgroup of .

From the given definition of , it is clear that

Since and are isomorphisms from some group to the same group,

Here, is the identity element. Therefore, . Thus, it is proved that is a nonempty subset of .

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