General Directions: Written assignments should be submitted typeset. What you submit must represent your own work.
Read these directions carefully: for each of the following statements either provide a proof that the statement is true or label the statement as false and provide justification.
Any group homomorphism where is a prime must either be the trivial homomorphism or else be an injective (one-to-one) map.
For any groups , any subgroup of , any group homomorphism , and any element one always has the equality of sets