On Burnside’s other p^aq^b theorem

George Isaac Glauberman

Vol. 56 (1975), No. 2, 469–476

DOI: 10.2140/pjm.1975.56.469

Abstract

Suppose G is a finite group whose order is divisible by only two primes. Burnside’s famous theorem asserts that G must be solvable. In a less famous theorem, Burnside gave sufficient conditions for G to have a nontrivial normal p-subgroup for a particular prime p. However, this theorem does not apply in certain cases when G has even order. In this paper, we prove an analogue of this theorem which applies to all cases.

Mathematical Subject Classification 2000

Primary: 20D10

Milestones

Received: 5 February 1974

Published: 1 February 1975