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On the Existence of a Noninner Automorphism of Order p for p-Groups

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Abstract

We obtain sufficient conditions for the existence of a noninner automorphism of order p for finite p-groups. We show that groups of order p n (n < 7, p is a prime number, p > 3) possess a noninner automorphism of order p.

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REFERENCES

  1. Kourovka Notebook [in Russian], Institute of Mathematics, Academy of Sciences of the USSR, Siberian Division, Novosibirsk (1980).

  2. L. Yu. Bodnarchuk and O. S. Pylyavs'ka, “Some classes of p-groups with an outer automorphism of order p,” Nauk. Zap. Nats. Univ. KMA, 18, No. 2, 372–374 (2000).

    Google Scholar 

  3. W. Gaschütz, “Nichtabelshe p-Gruppen basitzen ausere p-automorphismen,” J. Algebra, 4, 1–2 (1966).

    Google Scholar 

  4. B. Huppert, Endliche Gruppen, 1, Springer, Berlin (1967).

    Google Scholar 

  5. R. James, “The groups of order p 6 ( p is an odd prime),” Math. Comput., 34, No. 150, 613–637 (1980).

    Google Scholar 

  6. O. S. Pilyavskaya, “Classification of groups of order p 6, p > 3,” Dep. VINITI No. 1877–83 (1983).

  7. M. Hall, The Theory of Groups [Russian translation], Izd. Inostr. Lit., Moscow (1962).

    Google Scholar 

  8. P. Hall, “The classification of prime power groups,” J. Math., 182, 130–141 (1940).

    Google Scholar 

  9. T. A. Easterfield, Classification of Groups of Order p 6 , Ph. D. Thesis, Cambridge (1940).

  10. H. Neumann, Varieties of Groups [Russian translation], Mir, Moscow (1969).

    Google Scholar 

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Bodnarchuk, L.Y., Pylyavs'ka, O.S. On the Existence of a Noninner Automorphism of Order p for p-Groups. Ukrainian Mathematical Journal 53, 1771–1783 (2001). https://doi.org/10.1023/A:1015290510835

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  • DOI: https://doi.org/10.1023/A:1015290510835

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