Solution Found!
Suppose the and are isomorphisms of some group G to the
Chapter 6, Problem 49E(choose chapter or problem)
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 .