The classification of minimal non-prime-power order groups (Q1325226)

Finite groups all of whose proper subgroups are of prime power order are classified. The results are ``folklore'' and can easily be deduced from results of \textit{L. Rédéi} [Publ. Math. 4, 303-324 (1956; Zbl 0075.240)] on the structure of minimal nonnilpotent groups using standard Hall-Higman reduction [\textit{P. Hall} and \textit{G. Higman}, Proc. Lond. Math. Soc., III. Ser. 6, 1-42 (1956; Zbl 0073.255)]. The methods used in this paper, however, are completely elementary, so that the material can be presented in a graduate course in algebra.