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    Mann, Avinoam 1999. Some questions about p-groups. Journal of the Australian Mathematical Society, Vol. 67, Issue. 03, p. 356.

  • Proceedings of the Edinburgh Mathematical Society, Volume 30, Issue 1
  • February 1987, pp. 41-49

On the other pαqβ theorem of Burnside

  • Arie Bialostocki (a1)
  • DOI:
  • Published online: 01 January 2009

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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1.A. Bialostocki , On products of two nilpotent subgroups of a finite group, Israel J. Math. 20 (1975), 178188.

2.A. Bialostocki , The nilpotency class of the pSylow subgroups of GL(n, q) where (p, q) = l, Canad. Math. Bull. 29 (2) (1986), 218223.

4.R. Carter and P. Fong , The Sylow 2-subgroups of the finite classical groups, J. Algebra 1 (1964), 139151.

6.G. Glauberman , On Burnside's other pxqB theorem, Pacific J. Math. 56 (1975), 469475.

8.V. S. Monakhov , Order of Sylow subgroups of the general linear group, Algebra i Logika 17 (1978), 7985.

11.A. Weir , Sylow p-subgroups of the classical groups over finite fields with characteristic prime to p, Proc. Amer. Math. Soc. 6 (1955), 529533.

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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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