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Hi,

Given a dcpo of finitely presented groups, I wanted to say that the free group is bottom, but I don't think that is right. Can anyone say what is a typical bottom in a dcpo of groups? Furthermore, are the finitely presentable groups the finite or compact elements?

Best,

       Ben
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You should probably clarify what you mean by a typical dcpo of groups. Otherwise the bottom can be anything you want: just take the dcpo {G}... –  François G. Dorais Feb 24 '11 at 23:32
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Also, signatures (and greetings) aren't really necessary on MO. A signature is automatically attached to your posts. –  François G. Dorais Feb 24 '11 at 23:34
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What does "dcpo" mean? –  aaron Feb 25 '11 at 0:08
    
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Well, it's maximal if you think that a subgroup is greater than the group... which seems like an odd convention. –  HJRW Feb 25 '11 at 6:01
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