Groups of Hyperbolic Length in Odd Characteristic Groups of Lie Type Original Research Article

This work focuses on the maximum length of subgroup chain in an odd characteristic Lie type group G. If G does not have parabolic length, there exists a non-parabolic maximal subgroup M1, the length of which exceeds that every maximal parabolic subgroup P of G. The possible structure of such maximal subgroups is considered. In particular, it is shown that either M1 has known structure (listed in the main result), or there exists a maximal subgroup M of known structure having length equal to or greater than that of M1.