A generalized hughes property of finite groups

R. A. Bryce*, V. Fedri, L. Serena

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)


    A Hughes cover for exponent p (p a prime number) of a finite group is a union of subgroups whose (non-empty) complement consists of elements of order p. A proper Hughes subgroup is an instance of a Hughes cover; and its parent group is soluble by a well-known result of Hughes and Thompson. More generally an earlier result of the authors shows that a group with a Hughes cover of fewer than p subgroups is soluble. This article treats the insoluble groups having a Hughes cover for exponent p with exactly p subgroups: the almost simple groups with this property form a restricted class of projective special linear groups.

    Original languageEnglish
    Pages (from-to)4215-4243
    Number of pages29
    JournalCommunications in Algebra
    Issue number9
    Publication statusPublished - 1 Sept 2003


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