Zassenhaus lemma, Schreier refinement theorem and Jordan-Hölder theorem for gyrogroups (Q6546520)

The notion of a gyrogroup generalizes the notion of a group, namely for a gyrogroup a weaker version of the associative law holds. Gyrogroups are left Bol loops such that all left translations are automorphisms. In this paper, the authors extend the validity of the Zassenhaus lemma, the Schreier refinement theorem and the Jordan-Hörder theorem for gyrogroups. Their proofs differ from those given in [\textit{R. H. Bruck}, A survey of binary system. 3rd corr. printing. Berlin-Heidelberg-New York: Springer-Verlag (1971; Zbl 0206.30301)]. They also study subgyrogroup lattices.