Finite Groups of Chain Difference One,

A finite group G is said to have chain difference one if the lengths of any two unrefinable subgroup chains of G differ by at most one. Finite simple groups of chain difference one were classified by B. Brewster et al. (1993, J. Algebra160, 179–191) using the classification of finite simple groups. We give an more elementary proof of this result. In particular we give an elementary proof that a minimal counterexample has dihedral or semidihedral Sylow 2-subgroups.