Mark each of the following true or false.
_____ a. An is a normal subgroup of Sn.
_____ b. For any two groups G and G', there exists a homomorphism of G into G'.
_____ c. Every homomorphism is a one-to-one map.
_____ d. A homomorphism is one to one if and only if the kernel consists of the identity element alone.
_____ e. The image of a group of 6 elements under some homomorphism may have 4 elements. (Sec Exercise 44.)
_____ f. The image of a group of 6 elements under a homomorphism may have 12 elements.
_____ g. There is a homomorphism of some group of 6 elements into some group of 12 elements.
_____ h. There is a homomorphism of some group of 6 elements into some group of 10 elements.
_____ i. A homomorphism may have an empty kernel.
_____ j. It is not possible to have a nontrivial homomorphism of some finite group into some infinite group.
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