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Finite Groups Which are Automorphism Groups of Infinite Groups Only

Published online by Cambridge University Press:  20 November 2018

Jay Zimmerman
Jay Zimmerman*
Affiliation:
Department of Mathematics, Michigan State UniversityEast Lansing, MI 48824
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Abstract

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The object of this paper is to exhibit an infinite set of finite semisimple groups H, each of which is the automorphism group of some infinite group, but of no finite group. We begin the construction by choosing a finite simple group S whose outer automorphism group and Schur multiplier possess certain specified properties. The group H is a certain subgroup of Aut S which contains S. For example, most of the PSL's over a non-prime finite field are candidates for S, and in this case, H is generated by all of the inner, diagonal and graph automorphisms of S.

Keywords

20F2820E3620D45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 1 , 01 March 1985 , pp. 84 - 90
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Fuchs, L., Infinite Abelian Groups, Vol. II, Academic Press, New York (1973).Google Scholar
2. Robinson, D.J.S., A Course in the Theory of Groups, Springer-Verlag, New York (1982).Google Scholar
3. Robinson, D.J.S., Groups with prescribed automorphism group, Proc. Edinburgh Math. Soc. 25 (1982), pp. 217–227.Google Scholar
4. de Vries, H. and de Miranda, A. B., Groups with small number of automorphisms, Math Z. 68 (1958), pp. 450–464.Google Scholar