Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

On the other pαqβ theorem of Burnside

Arie Bialostockia1*

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)

Footnotes

* This paper forms part of the Proceedings of the conference Groups–St Andrews 1985.