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Thread: estimate number of groups

  1. #1
    Jun 2012

    Lightbulb estimate number of groups

    i need some upper estimate of number of groups of order 24. i know there are 15 of them, but i need upper estimate with explanation, it means why there cannot be more
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  2. #2
    Super Member girdav's Avatar
    Jul 2009
    Rouen, France

    Re: estimate number of groups

    Did you try an approach with Sylow theorems?
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  3. #3
    Nov 2011

    Re: estimate number of groups


    This problem is a triviality using Burnside's Lemma. Are you working out of Herstein, Cohn, Jacobson or Dummit-Foote? The Herstein and Jacobson do not treat this topic, but in the Cohn you can find it in the section on Group Actions. Same with Dummit-Foote. I do not immediately see a way to get an upper bound at precisely 15 without the use of Burnside's Lemma, however. For that it will be best to have a working knowledge of solvable groups.

    Edit: if this class has an emphasis on combinatorics, a Polya-Redfield equation could probably count it. But that would be more difficult than using the Burnside, and would still require knowledge of group actions (but not solvability criteria). Your choice!
    Last edited by skeptopotamus; Jun 8th 2012 at 09:14 PM.
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