Math Help - 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?

Originally Posted by pruzchett

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.

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...