8 research outputs found

    Minimal odd order automorphism groups

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    We show that 3^7 is the smallest order of a non-trivial odd order group which occurs as the full automorphism group of a finite group.Comment: 11 pages, no figures. Manuscript accepted for publicatio

    Counting commutativities in finite algebraic systems

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    We examine the total possible number of commutativities in a finite algebraic system, concentrating on groups, but also examining rings and semigroups. Numerical restrictions are found and bounds for the total number of commutativities in subgroups and factor groups are derived. Finally, a curious connection with group representations is explored

    Counting commutativities in finite algebraic systems

    No full text
    We examine the total possible number of commutativities in a finite algebraic system, concentrating on groups, but also examining rings and semigroups. Numerical restrictions are found and bounds for the total number of commutativities in subgroups and factor groups are derived. Finally, a curious connection with group representations is explored
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