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Solvable automorphism groups and an upper bound for $ A(G)$


Author: J. R. Weaver
Journal: Proc. Amer. Math. Soc. 27 (1971), 229-235
MSC: Primary 20.22
DOI: https://doi.org/10.1090/S0002-9939-1971-0271211-5
MathSciNet review: 0271211
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Abstract: The objective of this work is to find a subgroup $ H$ of a finite group $ G$ which will give information about the order of the automorphism group of $ G$ and the structure of the automorphism group of $ G$. An upper bound is found for the order of the automorphism group and conditions are given which insure that the automorphism group is solvable. Some information is given about a normal subgroup of a particular subgroup of the automorphism group. In this paper all groups are assumed to be finite.


References [Enhancements On Off] (What's this?)

  • [1] W. Gaschütz, Gruppen, in denen das Normalteilersein transitiv ist, J. Reine Angew. Math. 198 (1957), 87-92. MR 19, 940. MR 0091277 (19:940b)
  • [2] P. Hall, On the Sylow systems of a solvable group, Proc. London Math. Soc. 43 (1937), 316-323.
  • [3] H. Liebeck, The automorphism group of finite $ p$-groups, J. Algebra 4 (1966), 426-432. MR 34 #7653. MR 0207839 (34:7653)
  • [4] W. Wielandt, Topics in the theory of composite groups, Lecture Notes, Department of Mathematics, University of Wisconsin, Madison, Wis., 1967.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0271211-5
Keywords: Finite group, automorphism group, solvable, upper bound
Article copyright: © Copyright 1971 American Mathematical Society

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