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A group G has exactly 8 elements or order 3

  1. Jan 30, 2008 #1
    A group G has exactly 8 elements of order 3 (Unanswered as of 1/31)

    How many subgroups of order 3 does G have?

    So we have 8 elements, its prime decomposition is 8=2^3. The number of different ways to get factors is how many subgroups, at least that is what I interpret from my notes...so there are 2^3, 2*2^2, and 2*2*2, so three different ways to get factors, am I doing this right?

    Last edited: Jan 30, 2008
  2. jcsd
  3. Jan 30, 2008 #2
    Do you mean G has 8 elements OR order 3, or do you mean G has 8 elements OF order 3.
  4. Jan 30, 2008 #3
    g has 8 elements OF order 3, my bad
  5. Jan 31, 2008 #4


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    every subgroup of order three has how many elements of order three?

    and how many common elements of order three do two distinct subgroups of order three have?
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