The stabilizer subgroups of transitive \(l\)-permutation groups (Q2749005)

Let \(G\) be a lattice-ordered group. As a continuation of work of \textit{Z. Zhu} and \textit{Z. Huang} [Czech. Math. J. 49, 811-815 (1999)] and of \textit{Z. Zhu} and \textit{J. Huang} [J. Nanjing Univ., Math. Biq. 11, No. 1, 18-21 (1994; Zbl 0832.20004)], the authors prove that a transitive \(l\)-permutation group \(G\) is 2-transitive if and only if its stabilizer subgroup \(G_{(\Delta)}\) is transitive in the interval \(\{\Sigma\mid\Delta<\Sigma\},\) and if and only if for any \(\Delta<\Lambda<\Sigma\), there exists \(g\in G_{(\Delta)}\) such that \(\Sigma\leq \Lambda g.\) The authors also prove that an \(l\)-permutation group is normal-valued if and only if every primitive component is regular.