Vol. 56, No. 2, 1975

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On Burnside’s other paqb theorem

George Isaac Glauberman

Vol. 56 (1975), No. 2, 469–476

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
Received: 5 February 1974
Published: 1 February 1975
George Isaac Glauberman