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    Gow, Roderick Loewy, Raphael Queiró, João Filipe and Sergeichuk, Vladimir 2009. Preface. Linear Algebra and its Applications, Vol. 430, Issue. 7, p. 1725.
    1993. Nilpotent Groups and their Automorphisms.
    Kondrat'ev, A. S. Makhnev, A. A. and Starostin, A. I. 1989. Finite groups. Journal of Soviet Mathematics, Vol. 44, Issue. 3, p. 237.
    Khukhro, E. I. 1986. Finitep-groups that are close to groups of prime period. Algebra and Logic, Vol. 25, Issue. 2, p. 143.
    Espuelas, Alberto 1984. On the Hughes problem for exponentp 2. Archiv der Mathematik, Vol. 43, Issue. 5, p. 388.
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The Hughes problem for exponent nine

  • Thomas J. Laffey (a1)
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.

Copyright
COPYRIGHT: © Cambridge Philosophical Society 1980
References
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(1)Gorenstein, D.Finite Groups (New York, Harper and Row, 1968).
(2)Hughes, D. R. and Thompson, J. G.The Hp-problem and the structure of Hp-groups. Pacific Journal Math. 9 (1959), 1097–1101.
(3)Huppert, B.Endliche Gruppen Bd. i (Berlin, Heidelberg, New York, Springer-Verlag, 1967).
(4)Laffey, T. J.The number of solutions of x 3 = 1 in a 3-group. Math. Z. 149 (1976), 43–45.
(5)Laffey, T. J.The number of solutions of x 4 = 1 in a finite group. Proc. Roy. Irish Acad. 79, (1979), 29–36.
(6)Laffey, T. J.Algebras generated by two idempotents. Linear Algebra and Appl. (in the Press).
(7)Mordell, L. J.Diophantine equations (New York, Academic Press, 1969).
(8)Straus, E. G. and Szekeres, G.On a problem of D. R. Hughes. Proc. Amer. Math. Soc. 9 (1958), 157–158.
(9)Wall, G. E.Secretive p-groups of large rank. Bull. Austral. Math. Soc. 12 (1975), 363–369.
(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.)
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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