a1 Department of Mathematics and Statistics, University of Idaho, Moscow, Idaho, 83843, U.S.A.
The “other” pαqβ theorem of Burnside states the following:
Theorem A.l. Let G be a group of order pαqβ, where p and q are distinct primes. If pα>qβ, then Op(G)≠1 unless
(a) p is a Mersenne prime and q = 2;
(b) p = 2 and q is a Fermat prime; or
(c) p = 2 and q = 7.
(Received August 10 1985)
* This paper forms part of the Proceedings of the conference Groups–St Andrews 1985.