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Abstract algebra class equation

  1. Mar 16, 2017 #1
    1. The problem statement, all variables and given/known
    I
    f each element of a group, G, has order
    which is a power of p, then the order of G is also a prime power.

    2. Relevant equations


    3. The attempt at a solution
    I am not sure really where to get started. I know that the class equation will be used though
     
  2. jcsd
  3. Mar 16, 2017 #2

    Mark44

    Staff: Mentor

    How does your textbook define the phrase "order of a group"?
     
  4. Mar 16, 2017 #3
    The order of G is the number of elements in G
     
  5. Mar 16, 2017 #4

    Mark44

    Staff: Mentor

    And what is the order of an element of a group? It might be helpful to look at some examples, such as ##(\mathbb{Z_4}, *)## or ##(\mathbb{Z_5}, *)##.
     
  6. Mar 16, 2017 #5
    The order of an element of a group is the order of the cyclic subgroup that it generates.
     
  7. Mar 16, 2017 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Sure it is. I suggest you apply Cauchy's theorem to your group. Suppose the order of ##G## is NOT a power of ##p##?
     
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