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Math Help - isomorphismbetween groups

  1. #1
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    Lightbulb isomorphismbetween groups

    prove that if there is monomorphism from group A to group B and monomorphism from group B to group A than these two groups are isomorphic
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  2. #2
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    Re: isomorphismbetween groups

    this is false. let F2 be the free group on 2 letters (say a,b) and let F3 be the free group on 3 letters (say x,y,z).

    then a→x, b→y is a monomorphism of F2 into F3, and x→a2, y→ab and z→b2 is a monomorphism of F3 into F2, but these groups are NOT isomorphic.
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