Geodesic
Finite Groups Which are Automorphism Groups of Infinite Groups Only
Canadian mathematical bulletin, Tome 28 (1985) no. 1, pp. 84-90

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DOI

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.
DOI : 10.4153/CMB-1985-008-4
Mots-clés : 20F28, 20E36, 20D45 
Zimmerman, Jay. Finite Groups Which are Automorphism Groups of Infinite Groups Only. Canadian mathematical bulletin, Tome 28 (1985) no. 1, pp. 84-90. doi: 10.4153/CMB-1985-008-4
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     title = {Finite {Groups} {Which} are {Automorphism} {Groups} of {Infinite} {Groups} {Only}},
     journal = {Canadian mathematical bulletin},
     pages = {84--90},
     year = {1985},
     volume = {28},
     number = {1},
     doi = {10.4153/CMB-1985-008-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-008-4/}
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