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Prove that if G, H, and K are groups, and 8 : G -;. Hand : H -;. K are isomorphisms,then
Chapter 18, Problem 18.9(choose chapter or problem)
QUESTION:
Prove that if G, H, and K are groups, and 8 : G -;. Hand : H -;. K are isomorphisms,then 08 : G -;. K is an isomorphism. (Use multiplication for the group operations.)
Questions & Answers
QUESTION:
Prove that if G, H, and K are groups, and 8 : G -;. Hand : H -;. K are isomorphisms,then 08 : G -;. K is an isomorphism. (Use multiplication for the group operations.)
ANSWER:Step 1 of 2
Consider the groups and are isomorphisms.
To prove that is an isomorphism, we have to prove the following conditions,
1. is one-one
2. is onto
3. is homomorphism
As are isomorphisms, they are bisections, and hence their composition
is also bijective. Therefore the conditions (1),(2), are satisfied for