$n$-inner automorphisms of finite groups
HTML articles powered by AMS MathViewer
- by Fernando Szechtman PDF
- Proc. Amer. Math. Soc. 131 (2003), 3657-3664 Request permission
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 $n\geq 2$.References
- W. Burnside, On the outer automorphisms of a group, Proc. London Math. Soc. (2) 11 (1913), 40–42.
- Martin Hertweck, Class-preserving automorphisms of finite groups, J. Algebra 241 (2001), no. 1, 1–26. MR 1838841, DOI 10.1006/jabr.2001.8760
- Martin Hertweck, A counterexample to the isomorphism problem for integral group rings, Ann. of Math. (2) 154 (2001), no. 1, 115–138. MR 1847590, DOI 10.2307/3062112
- J.E. Humphreys, Introduction to L ie A lgebras and R epresentation T heory, Fifth ed., Springer-Verlag, New York, 1987.
- W. Kimmerle and K. W. Roggenkamp, Projective limits of group rings, J. Pure Appl. Algebra 88 (1993), no. 1-3, 119–142. MR 1233318, DOI 10.1016/0022-4049(93)90017-N
- Marcin Mazur, On the isomorphism problem for infinite group rings, Exposition. Math. 13 (1995), no. 5, 433–445. MR 1362869
- B. H. Neumann, Not quite inner automorphisms, Bull. Austral. Math. Soc. 23 (1981), no. 3, 461–469. MR 625186, DOI 10.1017/S0004972700007322
- Klaus W. Roggenkamp and Alexander Zimmermann, Outer group automorphisms may become inner in the integral group ring, J. Pure Appl. Algebra 103 (1995), no. 1, 91–99. MR 1354069, DOI 10.1016/0022-4049(95)90113-Y
- Chih Han Sah, “Automorphisms of finite groups” (J. Algebra 10 (1968), 47–68): addendum, J. Algebra 44 (1977), no. 2, 573–575. MR 435212, DOI 10.1016/0021-8693(77)90202-2
- Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
Additional Information
- Fernando Szechtman
- Affiliation: Department of Pure Mathematics, University of Waterloo, Ontario, Canada N2L 3G1
- Email: fszechtm@herod.uwaterloo.ca
- 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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 1998171