This quiz is about group element orders, cycle types of permutations, application of Sylow's theorem, and a question about group actions.
  1. How many of the following have order 6?
    • (1,2,4,7,3,6)
    • (7,5,1)(2,3)
    • (2,1,6)(2,3)
    • (1,2,3,7,5)(2,6)
    • (1,3,4)(2,5,7)
    Choices:
  2. Which of the following can't be the order of (a,b,c)(d,e) where a,b,c,d,e are not necessarily distinct integers, but a,b,c are distinct and d,e are distinct
    Choices:
  3. All element of order 6 in S7 have cycle type 61 or 21 31
    Choices:
  4. S5 has more elements of order 6 than A6
    Choices:
  5. Any element of order 6 in S7 is a product of an element of order 2 and an element of order 3
    Choices:
  6. A group of order 20 could contain 5 distinct subgroups of order 4
    Choices:
  7. All groups of order 17 are abelian
    Choices:
  8. All groups of order 16 are abelian
    Choices:
  9. All groups of order 15 are abelian
    Choices:
  10. A group of order 21 can not be simple
    Choices:
  11. which of the following can not act non trivially on {1,2,3,4}
    Choices: