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1-Hypergroups of Small Sizes

Author

Listed:
  • Mario De Salvo

    (Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98122 Messina, Italy)

  • Dario Fasino

    (Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, 33100 Udine, Italy)

  • Domenico Freni

    (Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, 33100 Udine, Italy)

  • Giovanni Lo Faro

    (Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98122 Messina, Italy)

Abstract

In this paper, we show a new construction of hypergroups that, under appropriate conditions, are complete hypergroups or non-complete 1-hypergroups. Furthermore, we classify the 1-hypergroups of size 5 and 6 based on the partition induced by the fundamental relation β . Many of these hypergroups can be obtained using the aforesaid hypergroup construction.

Suggested Citation

  • Mario De Salvo & Dario Fasino & Domenico Freni & Giovanni Lo Faro, 2021. "1-Hypergroups of Small Sizes," Mathematics, MDPI, vol. 9(2), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:108-:d:475613
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    Citations

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    Cited by:

    1. Christos Massouros & Gerasimos Massouros, 2021. "An Overview of the Foundations of the Hypergroup Theory," Mathematics, MDPI, vol. 9(9), pages 1-41, April.
    2. Christos G. Massouros & Naveed Yaqoob, 2021. "On the Theory of Left/Right Almost Groups and Hypergroups with their Relevant Enumerations," Mathematics, MDPI, vol. 9(15), pages 1-31, August.
    3. Irina Cristea & Milica Kankaraš, 2021. "The Reducibility Concept in General Hyperrings," Mathematics, MDPI, vol. 9(17), pages 1-14, August.

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