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  • Cited by 5
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Logan, Alan D. 2015. On the outer automorphism groups of finitely generated, residually finite groups. Journal of Algebra, Vol. 423, p. 890.


    Bludov, V. Droste, M. and Glass, A. 2011. Automorphism groups of totally ordered sets: A retrospective survey. Mathematica Slovaca, Vol. 61, Issue. 3,


    Bumagin, Inna and Wise, Daniel T. 2005. Every group is an outer automorphism group of a finitely generated group. Journal of Pure and Applied Algebra, Vol. 200, Issue. 1-2, p. 137.


    Braun, Gábor and Göbel, Rüdiger 2003. Outer automorphisms of locally finite p-groups. Journal of Algebra, Vol. 264, Issue. 1, p. 55.


    Giraudet, M. and Truss, J. K. 2003. Recovering ordered structures from quotients of their automorphism groups. The Journal of Symbolic Logic, Vol. 68, Issue. 04, p. 1189.


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  • Journal of the London Mathematical Society, Volume 64, Issue 3
  • December 2001, pp. 565-575

ALL GROUPS ARE OUTER AUTOMORPHISM GROUPS OF SIMPLE GROUPS

  • MANFRED DROSTE (a1), MICHÈLE GIRAUDET (a2) and RÜDIGER GÖBEL (a3)
  • DOI: http://dx.doi.org/10.1112/S0024610701002484
  • Published online: 01 January 2002
Abstract

It is shown that each group is the outer automorphism group of a simple group. Surprisingly, the proof is mainly based on the theory of ordered or relational structures and their symmetry groups. By a recent result of Droste and Shelah, any group is the outer automorphism group Out (Aut T) of the automorphism group Aut T of a doubly homogeneous chain (T, [les ]). However, Aut T is never simple. Following recent investigations on automorphism groups of circles, it is possible to turn (T, [les ]) into a circle C such that Out (Aut T) [bcong ] Out (Aut C). The unavoidable normal subgroups in Aut T evaporate in Aut C, which is now simple, and the result follows.

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Journal of the London Mathematical Society
  • ISSN: 0024-6107
  • EISSN: 1469-7750
  • URL: /core/journals/journal-of-the-london-mathematical-society
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