Sonlu Kanonik Hipergrupların SS-Tümlenmiş Althipergrupları Üzerine

Yıl 2025, Cilt: 25 Sayı: 4, 757 - 766, 04.08.2025

Sena Cam , Burcu Nişancı Türkmen , Yıldız Aydın

https://doi.org/10.35414/akufemubid.1565249

https://izlik.org/JA43RN75KX

Öz

Bu çalışmada literatürde var olan sonlu grupların SS-tümlenmiş altgrupları kavramı, sonlu kanonik hipergruplarda yorumlanmıştır. SS-tümlenmiş her althipergrubun althipergrubunda da ss-tümlenmiş olduğu görülmüştür. Hiperyapılarda çarpıcı bir sonuç olarak SS-tümlenmiş bir hipergrubun güçlü normal althipergruba göre her bölüm hipergrubunun SS-tümlenmiş olduğu ispatlanmıştır. Hipercebirsel yapı özelliklerinin çözülebilir hipergruplarda korunduğu görülmüştür. Böylece SS-tümleyen althipergruba sahip olma özelliği çözülebilir hipergruplarda karakterize edilmiştir.

Anahtar Kelimeler

Sonlu Kanonik Hipergrup , Güçlü Normal Althipergrup , ÇözülebilirAlthipergrup , SS-Tümlenmiş Althipergrup

On SS-Supplemented Subhypergroups of Finite Canonical Hypergroups

https://izlik.org/JA43RN75KX

Öz

In this study, the concept of SS-supplemented subgroups of finite groups existing in the literature is interpreted in finite canonical hypergroups. It has been observed that every SS-supplemented subhypergroup is also SS-supplemented in its subhypergroup. As a striking result in hyperstructures, it has been proven that every factor hypergroup of an SS-supplemented hypergroup is SS-supplemented compared to the strong normal subhypergroup. It has been observed that hyperalgebraic structure properties are preserved in solvable hypergroups. Thus, the property of having an SS-supplemented subhypergroup has been characterized in solvable hypergroups.

Anahtar Kelimeler

Finite Canonical Hypergroup , Strong Normal Subhypergroup , Solvable Hypergroup , SS-Supplemented Subhypergroup

Kaynakça

• Ballester Bolinches, A., Wang,Y., Xiuyun, G., 2000. C-supplemented subgroups of finite groups, Glasgow Mathematical Journal, 42(3), 383-389.
• Corsini, P., 1993. Prolegomena of Hypergroup Theory. Tricesimo: Aviani Editore. Corsini, P., Leoreanu, V., 2003. Applications of Hyperstructure Theory. Dordrecht: Kluwes Academical Publications.
• Davvaz, B., Leoreanu Fotea, V., 2007. Hyperring Theory and Applications, International Academic Press. Doerk, K., Hawkes, T., 1992. Finite Soluble Groups. Walter de Gruyter, Berlin. Gorenstein, D., 1968. Finite groups. Harper & Row, New York.
• Guo, X., Lu, J., 2012. On SS-supplemented subgroups of finite groups and their properties, Glasgow Mathematical Journal, 54(3), 481-491.
• Hall, P., 1937. A characteristic property of soluble groups, Journal of the London Mathematical Society, 12, 198-200.
• Hall,P., 1937. Complemented groups, Journal of the London Math. Soc., 12, 201-204. Jantani, F., Jafarpour, M., Mousavi, S. Sh., Leoreonu, V., 2017. On order of elements in hypergroups and p-Sylow subhypergroups, Communications in Algebra, 45(12), 5092-5102.
• Kegel, O., 1962. Sylow-gruppen und subnormalteiler endlicher gruppen, Mathematische Zeitschrift, 78(1), 205-221.
• Li, S., Shen, Z., Liu, J., Liu, X., 2008. The influence of SS_quasinormality of some subgroups on the structure of finite groups, Journal of Algebra, 319, 4275-4287.
• Marty,F., 1934. Sur une Generalization de la Nation de Groupe. 8 th Congress Mathematics Scandenaves, Stockholm, Sweden, 45-49.
• Vasil’ev, A., Zieschang, P.H., 2022. Solvable hypergroups and a generalization of Hall's theorems on solvable groups to assoriation schemes, Journal of Algebra, 594, 733-750.
• Vougiouklis,T., 1994. Hyperstructures and Their Representations. Palm Harbor, FL: Hadronic Press.