inner automorphisms of finite groups
Author:
Fernando Szechtman
Journal:
Proc. Amer. Math. Soc. 131 (2003), 36573664
MSC (2000):
Primary 20D45, 20E36
Published electronically:
February 28, 2003
MathSciNet review:
1998171
Fulltext 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 2inner 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), 4042.
 [Her01a]
Martin
Hertweck, Classpreserving automorphisms of finite groups, J.
Algebra 241 (2001), no. 1, 1–26. MR 1838841
(2002e:20047), http://dx.doi.org/10.1006/jabr.2001.8760
 [Her01b]
Martin
Hertweck, A counterexample to the isomorphism problem for integral
group rings, Ann. of Math. (2) 154 (2001),
no. 1, 115–138. MR 1847590
(2002e:20010), http://dx.doi.org/10.2307/3062112
 [Hum87]
J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Fifth ed., SpringerVerlag, New York, 1987.
 [KR93]
W.
Kimmerle and K.
W. Roggenkamp, Projective limits of group rings, J. Pure Appl.
Algebra 88 (1993), no. 13, 119–142. MR 1233318
(94f:20008), http://dx.doi.org/10.1016/00224049(93)90017N
 [Maz95]
Marcin
Mazur, On the isomorphism problem for infinite group rings,
Exposition. Math. 13 (1995), no. 5, 433–445. MR 1362869
(96k:20007)
 [Neu81]
B.
H. Neumann, Not quite inner automorphisms, Bull. Austral.
Math. Soc. 23 (1981), no. 3, 461–469. MR 625186
(82i:20039), http://dx.doi.org/10.1017/S0004972700007322
 [RZ95]
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
(97b:20004), http://dx.doi.org/10.1016/00224049(95)90113Y
 [Sah68]
Chih
Han Sah, “Automorphisms of finite groups” (J. Algebra
10 (1968), 47–68): addendum, J. Algebra 44
(1977), no. 2, 573–575. MR 0435212
(55 #8172)
 [Wal47]
G.
E. Wall, Finite groups with classpreserving outer
automorphisms, J. London Math. Soc. 22 (1947),
315–320 (1948). MR 0025461
(10,8g)
 [Bur13]
 W. Burnside, On the outer automorphisms of a group, Proc. London Math. Soc. (2) 11 (1913), 4042.
 [Her01a]
 M. Hertweck, Classpreserving automorphisms of finite groups, J. Algebra 241 (2001), 126. MR 2002e:20047
 [Her01b]
 M. Hertweck, A counterexample to the isomorphism problem for integral group rings, Ann. of Math. (2) 154 (2001), 115138. MR 2002e:20010
 [Hum87]
 J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Fifth ed., SpringerVerlag, New York, 1987.
 [KR93]
 W. Kimmerle and K.W. Roggenkamp, Projective limits of group rings, J. Pure Appl. Algebra 88 (1993), 119142. MR 94f:20008
 [Maz95]
 M. Mazur, On the isomorphism problem for integral group rings, Exposition. Math. 13 (1995), 433445. MR 96k:20007
 [Neu81]
 B. Neumann, Not quite inner automorphisms, Bull. Austral. Math. Soc. 23 (1981), 461469. 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), 9199. MR 97b:20004
 [Sah68]
 C.H. Sah, Automorphisms of finite groups, J. Algebra 10 (1968), 4768. MR 55:8172
 [Wal47]
 G.E. Wall, Finite groups with classpreserving outer automorphisms, J. London Math. Soc. 22 (1947), 315320. MR 10:8g
Similar Articles
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:
http://dx.doi.org/10.1090/S0002993903069740
PII:
S 00029939(03)069740
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
