BIROn - Birkbeck Institutional Research Online

    A question of Zhou, Shi and Duan on nonpower subgroups of finite groups

    Anabanti, Chimere and Aroh, A.B. and Hart, Sarah and Oodo, A.R. (2021) A question of Zhou, Shi and Duan on nonpower subgroups of finite groups. Quaestiones Mathematicae , ISSN 1607-3606. (In Press)

    [img] Text
    AHAO_A question of Zhou Shi and Duan on nonpower subgroups of finite groups.pdf - Author's Accepted Manuscript
    Restricted to Repository staff only

    Download (285kB)
    [img]
    Preview
    Text
    44179a.pdf - Published Version of Record
    Available under License Creative Commons Attribution.

    Download (528kB) | Preview

    Abstract

    A subgroup H of a group G is called a power subgroup of G if there exists a non-negative integer m such that H= <g^m : g in G>. Any subgroup of G which is not a power subgroup is called a nonpower subgroup of G. Zhou, Shi and Duan, in a 2006 paper, asked whether for every integer k (with k at least 3), there exist groups possessing exactly k nonpower subgroups. We answer this question in the affirmative by giving an explicit construction that leads to at least one group with exactly k nonpower subgroups, for all k greater than or equal to 3, and infinitely many such groups when k is composite and greater than 4. Moreover, we describe the number of nonpower subgroups for the cases of elementary abelian groups, dihedral groups, and 2-groups of maximal class.

    Metadata

    Item Type: Article
    Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis, available online at the link above.
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hart
    Date Deposited: 12 May 2021 10:44
    Last Modified: 23 Jul 2021 17:36
    URI: https://eprints.bbk.ac.uk/id/eprint/44179

    Statistics

    Downloads
    Activity Overview
    3Downloads
    53Hits

    Additional statistics are available via IRStats2.

    Archive Staff Only (login required)

    Edit/View Item Edit/View Item