Basically I'm trying to revise for my thursday exam and it's going terribly. I am struggling with these two questions....
Let X, Y be the permutations:...
X = (1 2 3 4 5 6 7) and
----(1 5 7 4 6 2 3)
Write X, Y, X^3, XY as products of disjoint cycles and determine orders plus signs!
I really need a 'dummies' guide so to speak to this one. And X is written exactly like that with the numbers above and below.
The next question is:
Let f: Z5 -> Z5 be given by - draw the diagram of f and determine wether its injective or surjective. Justify.
part ii) Give an example of a three element subset A -> Z5 such that the restriction of f to A is injective.
part iii) give an example of subsets B,C such that f takes each element of B to B and the resulting map is surjective.
These are the two questions I am currently stuck on, if anyone can offer advice to either one I reserve alot of thanks for you. I'm pretty sure I might need help on other questions but not until I have figured these out. Thanks alot in advance.