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Groups with prescribed automorphism group

Published online by Cambridge University Press:  20 January 2009

Derek J. S. Robinson
Derek J. S. Robinson
Affiliation:
Department of Mathematics, University of Illinois, Urbana Illinois 61801, U.S.A.
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We are concerned here with question: to what extent can the structure of a group G be recaptured from information about the structure of its group of automorphismsAut G? For example, one might try to find all groups which have some specific group astheir (full) automorphism group, a point of view adopted by Iyer in a recent paper [5]. Nothing is known about this question in general except the result of Nagrebeckü [7] that there are only finitely many finite groups with a given group as automorphismgroup.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 3 , October 1982 , pp. 217 - 227
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

REFERENCES

1.Alperin, J. L. and Gorenstein, D., The multiplicators of certain simple groups, Proc. Amer. Math. Soc. 17 (1966), 515–519.CrossRefGoogle Scholar
2.Artin., E., The orders of the classical simple groups, Coram. Pure Appl. Math. 8 (1955), 455–472.CrossRefGoogle Scholar
3.Griess, R. L., Schur multipliers of the known finite simple groups I, II, Bull. Amer. Math. Soc. 78 (1972), 68–71.CrossRefGoogle Scholar
Proc. Symposia Pure Math. 37 (1980), 279–282.Google Scholar
4.Hallett, J. T. and A.Hirsch, K., Torsion-free groups having finite automorphism groups I, J. Algebra 2 (1965), 287–298.CrossRefGoogle Scholar
5.Iyer, H., On solving the equation Aut(X) = G, Rocky Mountain J. Math. 9 (1979), 653–670.CrossRefGoogle Scholar
6.Miller, G. A., On the groups which have the same group of isomorphisms, Trans. Amer. Math. Soc. 1 (1900), 395–401.Google Scholar
7.Nagrebecki, V. T., On groups with a finite number of automorphisms, Mat. Sb. 86 (1971), 571–577 = Math. USSR—Sb 15 (1971), 568–575.Google Scholar
8.Nagrebeckil, V. T., On the periodic part of a group with a finite number of automorphisms, Dokl. Akad. Nauk SSSR 205 (1972), 519–521 = Soviet Math. Dokl. 13 (1972), 953–956.Google Scholar
9.Robinson, D. J. S.. A contribution to the theory of groups with finitely many automorphisms, Proc. London Math. Soc. (35 (1977), 34–54.CrossRefGoogle Scholar
10.Robinson, D. J. S.. Infinite torsion groups as automorphism groups, Quart. J. Math. (2) 30 (1979), 351–364.CrossRefGoogle Scholar
11.Stammbach., U., Homology in Group Theory (Lecture Notes in Mathematics Vol. 359, Springer, Berlin, 1973).CrossRefGoogle Scholar