A Reduction Theorem for the Chain Length of an Odd Characteristic Lie Type Group Original Research Article

The focus of this work is the study of the length of a finite group of Lie type in arbitrary odd characteristic. If such a Lie type group G does not have parabolic length, there is a non-parabolic maximal subgroup M whose length strictly exceeds that of every parabolic subgroup P of G. Such maximal subgroups M with a subnormal quasisimple Lie type group S which is in the natural characteristic are considered. In particular, it is shown that S must possess a non-parabolic maximal subgroup M0, the length of which strictly exceeds that of every parabolic subgroup of S.