-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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We refer to an automorphism of a group as -inner if given any subset of with cardinality less than , there exists an inner automorphism of agreeing with on . Hence is 2-inner if it sends every element of to a conjugate. New examples are given of outer -inner automorphisms of finite groups for all natural numbers .

**[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**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
20D45,
20E36

Retrieve articles in all journals with MSC (2000): 20D45, 20E36

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