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The Hughes problem for exponent nine

Published online by Cambridge University Press:  24 October 2008

Thomas J. Laffey
Thomas J. Laffey
Affiliation:
University College, Dublin
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Extract

Let G be a finite group and n a natural number. Set Hn(G) = ≺g ∈ G|gn ≠ 1≻. The aim of this paper is to prove the following result.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 3 , May 1980 , pp. 393 - 399
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

REFERENCES

(1)Gorenstein, D.Finite Groups (New York, Harper and Row, 1968).Google Scholar
(2)Hughes, D. R. and Thompson, J. G.The Hp-problem and the structure of Hp-groups. Pacific Journal Math. 9 (1959), 1097–1101.CrossRefGoogle Scholar
(3)Huppert, B.Endliche Gruppen Bd. i (Berlin, Heidelberg, New York, Springer-Verlag, 1967).CrossRefGoogle Scholar
(4)Laffey, T. J.The number of solutions of x 3 = 1 in a 3-group. Math. Z. 149 (1976), 43–45.CrossRefGoogle Scholar
(5)Laffey, T. J.The number of solutions of x 4 = 1 in a finite group. Proc. Roy. Irish Acad. 79, (1979), 29–36.Google Scholar
(6)Laffey, T. J.Algebras generated by two idempotents. Linear Algebra and Appl. (in the Press).Google Scholar
(7)Mordell, L. J.Diophantine equations (New York, Academic Press, 1969).Google Scholar
(8)Straus, E. G. and Szekeres, G.On a problem of D. R. Hughes. Proc. Amer. Math. Soc. 9 (1958), 157–158.CrossRefGoogle Scholar
(9)Wall, G. E.Secretive p-groups of large rank. Bull. Austral. Math. Soc. 12 (1975), 363–369.CrossRefGoogle Scholar
(10)Wall, G. E.On Hughes Hp-problem. Article in Proc. of the International Conference, on the Theory of Groups (Canberra, 1965). (New York, Gordon and Breach, 1967.)Google Scholar