Answers, Midterm exam 2006:

Problem 1: A and C are groups
Problem 2: There are 5 groups
Problem 3: The order is 12
Problem 4: sigma=(6472)(13)
Problem 5: The index is 30
Problem 6: There are 4 proper, non-trivial subgroups
Problem 7: phi1 and phi3 are homomorphisms
Problem 8: B and D are the correct statements
Problem 9: 25 colourings remain the same
Problem 10: There are 35 different ways