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Free products of groups have no outer normal automorphisms

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Abstract

An automorphism of an arbitrary group is called normal if all subgroups of this group are left invariant by it. Lubotski [1] and Lue [2] showed that every normal automorphism of a noncyclic free group is inner. Here we prove that every normal automorphism of a nontrivial free product of groups is inner as well.

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References

  1. A. Lubotski, “Normal automorphisms of free groups,”J. Alg.,63, No. 2, 494–498 (1980).

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  2. A. S.-T. Lue, “Normal automorphisms of free groups,”J. Alg.,64, No. 1, 52–53 (1980).

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  3. R. Lyndon and P. Schupp,Combinatorial Group Theory, Springer, New York (1977).

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  4. M. I. Kargapolov and Yu. I. Merzlyakov,Foundations of Group Theory [in Russian], Nauka, Moscow (1982).

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Authors
  1. M. V. Neshadim
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Additional information

Supported by RFFR grant No. 13-011-1513.

Translated fromAlgebra i Logika, Vol. 35, No. 5, pp. 562–566, September–October, 1996.

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Neshadim, M.V. Free products of groups have no outer normal automorphisms. Algebr Logic 35, 316–318 (1996). https://doi.org/10.1007/BF02367356

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  • DOI: https://doi.org/10.1007/BF02367356

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