0
$\begingroup$

Given a directed-complete partial order of finitely presented groups, I want to say that the free group is the bottom, but I don't think that is right.

Can anyone say what is a typical bottom in a directed-complete partial order of groups? Furthermore, are the finitely presentable groups the finite or compact elements?

Improve this question
$\endgroup$
16
  • 4
    $\begingroup$ 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}... $\endgroup$
    – François G. Dorais
    Commented Feb 24, 2011 at 23:32
  • 1
    $\begingroup$ Also, signatures (and greetings) aren't really necessary on MO. A signature is automatically attached to your posts. $\endgroup$
    – François G. Dorais
    Commented Feb 24, 2011 at 23:34
  • 2
    $\begingroup$ What does "dcpo" mean? $\endgroup$
    – aaron
    Commented Feb 25, 2011 at 0:08
  • 2
    $\begingroup$ Well, it's maximal if you think that a subgroup is greater than the group... which seems like an odd convention. $\endgroup$
    – HJRW
    Commented Feb 25, 2011 at 6:01
  • 1
    $\begingroup$ @SeanLawton your change to the title has actually made it incorrect. One should speak of a DCPO of groups, not of "DCPO groups". Moreover, why not insert the definite or indefinite article before the word "bottom" if you feel these changes are so necessary as to warrant bumping this question? $\endgroup$
    – Yemon Choi
    Commented Jun 4, 2016 at 14:02

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .