IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i7p1018-d1366025.html
   My bibliography  Save this article

A Characterization of Procyclic Groups via Complete Exterior Degree

Author

Listed:
  • Bernardo G. Rodrigues

    (Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield, Pretoria 0028, South Africa)

  • Francesco G. Russo

    (Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X1, Rondebosch, Cape Town 7701, South Africa
    Department of Mathematics and Applied Mathematics, University of the Western Cape, New CAMS Building, Private Bag X17, Bellville 7535, South Africa)

Abstract

We describe the nonabelian exterior square G ∧ ^ G of a pro- p -group G (with p arbitrary prime) in terms of quotients of free pro- p -groups, providing a new method of construction of G ∧ ^ G and new structural results for G ∧ ^ G . Then, we investigate a generalization of the probability that two randomly chosen elements of G commute: this notion is known as the “complete exterior degree” of a pro- p -group and we will use it to characterize procyclic groups. Among other things, we present a new formula, which simplifies the numerical aspects which are connected with the evaluation of the complete exterior degree.

Suggested Citation

  • Bernardo G. Rodrigues & Francesco G. Russo, 2024. "A Characterization of Procyclic Groups via Complete Exterior Degree," Mathematics, MDPI, vol. 12(7), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1018-:d:1366025
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/7/1018/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/7/1018/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1018-:d:1366025. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.