Hi, I am in difficulty when I kept trying to do these questions.

Could you give me a help to solve these questions?

Thank you so much.

Q1: Consider the permutation group 37. (a) Can the product of two cycles of length 4 be a cycle of length 6? (b) Can the product of two cycles of length 4 be a cycle of length 7'? Q2: What fraction of the permutations in Sn are cycles of length 71? Q3: Consider two types of triangle: equilateral and isoceles, as depicted: A A C B C B (a) Describe the (rigid) symmetries of an equilateral triangle. (b) Which of the symmetries in part (a) would also be a symmetry of the isoceles tri- angle? Using your answer, justify or refute the following statement: \"Equilateral triangles are more symmetric than isoceles triangles.\