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Subnormality and Thin Residues

In: Hypergroups

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  • Paul-Hermann Zieschang

    (University of Texas Rio Grande Valley, School of Mathematical & Statistical Sciences)

Abstract

We start this chapter with the definition of subnormal chains. General properties of subnormal chains will be compiled in Section 4.1. In Section 4.2, we restrict our attention to subnormal series. (Subnormal series are subnormal chains which contain {1}.) Maximal subnormal series of hypergroups will be called composition series, and composition series will be in the center of Section 4.3. With the help of the Second Isomorphism Theorem (Theorem 3.7.3) we will see (in Theorem 4.3.2) that any two composition series of a given hypergroup are isomorphic. This leads to the notion of a composition factor of a hypergroup and underscores the importance of simple hypergroups.

Suggested Citation

  • Paul-Hermann Zieschang, 2023. "Subnormality and Thin Residues," Springer Books, in: Hypergroups, chapter 4, pages 91-119, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-39489-8_4
    DOI: 10.1007/978-3-031-39489-8_4
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