Assignment:
Recall that S0 denotes the symmetric group of degree 6, the group of permutations f the numbers 1 to 6. let
Thus : {1, 2 3, 4, 5, 6} {1, 2, 3, 4, 5, 6} is a bijection, mapping 1 to 3, 2 to 5, etc. let
• Compute σ-1 and σπ and write them also b array form. (don’t forget that, as we write maps in the left , σπ means do π and then σ , so σπ(1) =σ(6) = 6 and so on)
• Compute the order of σ.
• Elements of Sn can be written in an alternative form, called cycle notation. Starting with 1, we see that σ(1) = 3 σ(4) = 1, back to the start. So the first cycle for σ is (1 3 4). As this has 3 numbers, it is called 3-cycle. Next, we take a number not yet mentioned, e.g, 2. we see that σ(2) = 5 and σ(5) = 2. So the next cycle for σ is (2 5). Finally we get a 1-cycle, (6). We write σ= (1, 3 ,4)(2, 5)(6). Write π in cycle notation.
Provide complete and step by step solution for the question and show calculations and use formulas.