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On the other pαqβ theorem of Burnside

  • Arie Bialostocki (a1)
Abstract

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.

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References
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1.Bialostocki A., On products of two nilpotent subgroups of a finite group, Israel J. Math. 20 (1975), 178188.
2.Bialostocki A., The nilpotency class of the pSylow subgroups of GL(n, q) where (p, q) = l, Canad. Math. Bull. 29 (2) (1986), 218223.
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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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