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$n$-inner automorphisms of finite groups


Author: Fernando Szechtman
Journal: Proc. Amer. Math. Soc. 131 (2003), 3657-3664
MSC (2000): Primary 20D45, 20E36
DOI: https://doi.org/10.1090/S0002-9939-03-06974-0
Published electronically: February 28, 2003
MathSciNet review: 1998171
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Abstract: We refer to an automorphism $g$ of a group $G$ as $n$-inner if given any subset $S$ of $G$ with cardinality less than $n$, there exists an inner automorphism of $G$ agreeing with $g$ on $S$. Hence $g$ is 2-inner if it sends every element of $G$ to a conjugate. New examples are given of outer $n$-inner automorphisms of finite groups for all natural numbers $n\geq 2$.


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  • [Bur13] W. Burnside, On the outer automorphisms of a group, Proc. London Math. Soc. (2) 11 (1913), 40-42.
  • [Her01a] M. Hertweck, Class-preserving automorphisms of finite groups, J. Algebra 241 (2001), 1-26. MR 2002e:20047
  • [Her01b] M. Hertweck, A counterexample to the isomorphism problem for integral group rings, Ann. of Math. (2) 154 (2001), 115-138. MR 2002e:20010
  • [Hum87] J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Fifth ed., Springer-Verlag, New York, 1987.
  • [KR93] W. Kimmerle and K.W. Roggenkamp, Projective limits of group rings, J. Pure Appl. Algebra 88 (1993), 119-142. MR 94f:20008
  • [Maz95] M. Mazur, On the isomorphism problem for integral group rings, Exposition. Math. 13 (1995), 433-445. MR 96k:20007
  • [Neu81] B. Neumann, Not quite inner automorphisms, Bull. Austral. Math. Soc. 23 (1981), 461-469. MR 82i:20039
  • [RZ95] K.W. Roggenkamp and A. Zimmermann, Outer group automorphisms may become inner in the integral group ring, J. Pure Appl. Algebra 103 (1995), 91-99. MR 97b:20004
  • [Sah68] C.H. Sah, Automorphisms of finite groups, J. Algebra 10 (1968), 47-68. MR 55:8172
  • [Wal47] G.E. Wall, Finite groups with class-preserving outer automorphisms, J. London Math. Soc. 22 (1947), 315-320. MR 10:8g

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Additional Information

Fernando Szechtman
Affiliation: Department of Pure Mathematics, University of Waterloo, Ontario, Canada N2L 3G1
Email: fszechtm@herod.uwaterloo.ca

DOI: https://doi.org/10.1090/S0002-9939-03-06974-0
Received by editor(s): March 6, 2002
Received by editor(s) in revised form: July 10, 2002
Published electronically: February 28, 2003
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2003 American Mathematical Society

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