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Math Help - Free Groups

  1. #1
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    Free Groups

    hi everyone. my problem is with free groups and group presentations.

    if say, for example, i have a group <a,b,c | ab=c & some other relations> is this group necessarily isomorphic to a group <d,e,f | de=f and some relations> if the relations in the second group are similar in form with the first one?
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  2. #2
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    Quote Originally Posted by pruzchett View Post
    hi everyone. my problem is with free groups and group presentations.

    if say, for example, i have a group <a,b,c | ab=c & some other relations> is this group necessarily isomorphic to a group <d,e,f | de=f and some relations> if the relations in the second group are similar in form with the first one?
    yes.
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  3. #3
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    thanks for the reply, is there a theorem on this or anything? i badly need it for my thesis and i couldn't find a book that examines the isomorphism of nonabelian free groups with similar structure of relators thoroughly...
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