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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?


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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
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
What does "dcpo" mean? – aaron Feb 25 '11 at 0:08
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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