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Show <a in D8 : a^2=1> is not a group

  1. Mar 18, 2012 #1

    I've been trying to solve this question,

    Show that <a in D8 : a2=1> is a not a group.

    I might not be processing it properly, but my interpretation of the question is that

    <a in D8 : a2=1> = <(a,b): a2=e, b2=2, ab=a-1b>

    Which is just D4, a group, the set of dihedral where 2n=4,

    Is the proper interpretation supposed to be

    <a in D8 : a2=1> = <(a,b): a2=e, a4=e,b2=2, ab=a-1b>

    which is again D4,

    Could anyone help me interoperate the question
  2. jcsd
  3. Mar 18, 2012 #2


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    Gold Member

    Notice that D8 = {e,r,r2,r3,s,sr,sr2,sr3}. Now check which of these elements have order 2. Then find two elements of order 2 which when multiplied together do not produce an element of order 2.
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