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On the other pαqβ theorem of Burnside

Published online by Cambridge University Press:  20 January 2009

Arie Bialostocki
Arie Bialostocki
Affiliation:
Department of Mathematics and Statistics, University of Idaho, Moscow, Idaho, 83843, U.S.A.
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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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 1 , February 1987 , pp. 41 - 49
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

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