1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How many elements of order 5 are in S7?

  1. Oct 5, 2004 #1
    Greetings, I just stumbled upon this site and thought someone might be able to help me. How many elements of order 5 are in S7? Are the elements permutations? I thought that S7 was a permutation of order 7. Also, are permutations cyclic groups? I know that permutations are a group and can be written as cycles ,but is this "cycle" the same as a "cyclic" group? Do these questions make any sense? :confused:
  2. jcsd
  3. Oct 6, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    S_7 is the set of all permutations of 7 objects. I've never seen S7 written to be honest, they tend to use subscripts.

    'are permutations cyclic groups' is no, since one is an element of a group, and one is a group.

    A cyclic group is one generated by a single element.

    Given a cycle in S_n it generates a cyclic subgroup, which is a proper subgroup unless n=2.

    In usual notation, a cycle is something of the form (abc...d), and any permutation is writable as a product of disjoint cycles, that is cycles that have no common elements. eg (123)(45) is a product of disjoint cycles, but (12)(23) isn't. It is equal to (123).

    A cycle with n elements in it has order n.

    The product of two disjoint cycles of lengths p and q has order lcm(p,q)

    this is enough to find all the elements of S_7 that have order 5.
  4. Oct 6, 2004 #3
    Thank you, matt! your answer is really helpful for my present study! I hope people would feel the same..:niceteeth:
    Oh, sorry so unbearable that I have to :biggrin:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?