Section SolvablePrimeFactor.
Variables (gT : finGroupType) (G : {group gT}).

(* Specifications: *)
Lemma index_maxnormal_sol_prime (H : {group gT}) :
solvable G -> maxnormal H G G -> prime #|G : H|.
Lemma sol_prime_factor_exists :
solvable G -> G :!=: 1 -> {H : {group gT} | H <| G & prime #|G : H| }.