MTH376 Algebra

Assignment # 3(Lectures 21-25)

Deadline: Midnight, Friday, June 5, 2015

Instructions:Make the assignment yourself. Try the questions as best you can.Do not copy the work of others or from any other source.Do not share your work with anyone or on any social networks.You may either type your solutions or write your assignment on paper and submit a scannedcopy.Attempt all questions.

Question 1 (5 marks)Dene and give an example of each of the following.

a) Homomorphismb) Isomorphismc) Monomorphismd) Epimorphisme) Endomorphismf) Automorphism

Question 2 (5 marks)Prove that if ' is an isomorphism from a group G1 to G2 and

a) If H is a subgroup of G1, then '(H) is a subgroup of G2.b) If G1 is cyclic then G2 is also cyclic.

Good Luck!

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