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The Number of Isomorphism Classes of D. G. Near-Rings on the Generalized Quaternion Groups

In: Near-Rings and Near-Fields

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  • Christof Nöbauer

    (Johannes Kepler Universität Linz, Institut für Algebra, Stochastik und wissensbasierte mathematische Systeme)

Abstract

Let Q n be the generalized quaternion group of order 2 n . In 1972, Malone ([Mal72], Theorem 7) determined that exactly 16 d.g. near-rings can be defined on Q n and that all of these are in fact distributive. However, as Clay pointed out ([Cla74]), “nothing is said concerning the isomorphism of these 16.” We show in this note that there are exactly 10 non-isomorphic d.g. near-rings on Q n for n ≥ 4 and 6 if n = 3.

Suggested Citation

  • Christof Nöbauer, 2001. "The Number of Isomorphism Classes of D. G. Near-Rings on the Generalized Quaternion Groups," Springer Books, in: Yuen Fong & Carl Maxson & John Meldrum & Günter Pilz & Andries van der Walt & Leon van Wyk (ed.), Near-Rings and Near-Fields, pages 133-137, Springer.
    • Handle: RePEc:spr:sprchp:978-94-010-0954-6_16
    DOI: 10.1007/978-94-010-0954-6_16
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