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Homework Help: Abstract algebra

  1. Apr 4, 2010 #1
    1. The problem statement, all variables and given/known data

    If |a^2|=|b^2|, prove or disprove that |a|=|b|.

    2. Relevant equations
    The hint I was given is that let a be an element of order 4n+2 and let the order of b=a2

    3. The attempt at a solution
    I can disprove this by looking at examples, such as in the group Z20 with letting a =2 and b=4, the |a|=10 and |b|=5, but |a^2|=5 and |b^2|=5. But I know that this does not disprove it for all groups, I need a more general solution. If anyone can help me on this it would be great.
  2. jcsd
  3. Apr 4, 2010 #2


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    Staff Emeritus
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    Gold Member

    I'm going to go on a limb and say the statement is true for some groups (for example in Z3). When they say to disprove a conjecture, all that means is find a counterexample.
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