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On finite groups of exponent five

Published online by Cambridge University Press:  24 October 2008

Graham Higman
Graham Higman
Affiliation:
The Mathematical Institute10 Parks RoadOxford
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Extract

1. The object of this note is to prove the restricted Burnside conjecture for exponent 5, that is, to prove, for n = 5, the proposition:

Rn: For each positive integer k there is an integer rn, k such that every finite group of exponent n that can be generated by k elements has order at most rn, k.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 3 , July 1956 , pp. 381 - 390
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

(1)Hall, P. and Higman, G.The p-length of a p-soluble group, and reduction theorems for Burnside's problem. Proc. Lond. math. Soc. (3) 7 (1956), 1–42.Google Scholar
(2)Higgins, P. J.Lie rings satisfying the Engel condition. Proc. Camb. phil. Soc. 50 (1954), 8–15.CrossRefGoogle Scholar
(3)Kostrikin, A. I.Solution of the restricted Burnside problem for exponent 5. Izvestiya Akad. Nauk SSSR, Ser. mat., 19 (1955), 233–244 (in Russian).Google Scholar
(4)Lazard, M.Sur les groupes nilpotents et les anneaux de Lie. Ann. sci. Éc. norm. sup., Paris, (3) 71 (1954), 101–190.CrossRefGoogle Scholar