Finite p'-nilpotent groups. II (Q1089429)

The author continues his investigation of finite p'-nilpotent groups [Part I, ibid. 10, 135-146 (1987; Zbl 0614.20009)]. (A group is said to be p'-nilpotent if it has a normal Sylow p-subgroup with nilpotent complement; so it is p'-nilpotent if and only if it is q-nilpotent for all primes \(q\neq p.)\) The main theorem of the paper characterizes the nonsolvable simple groups in which each proper subgroup is q'-nilpotent for some prime q. (For example, each proper subgroup of \(A_ 5\) is either 2'-nilpotent, 3'-nilpotent or 5'-nilpotent.) The proof uses Thompson's classification of the minimal simple groups and Dickson's list of all the subgroups of \(PSL(2,p^ n)\).