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Semi-invariants and weights of group algebras of finite groups

Author(s): D. S. Passman; P. Wauters
Journal: Proc. Amer. Math. Soc. 127 (1999), 1323-1329.
MSC (1991): Primary 16S34, 20D15, 20D45
Posted: February 4, 1999
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Abstract: We study the semi-invariants and weights of a group algebra $K[G]$ over a field $K$ of characteristic zero. Specifically, we show that certain basic results which hold when $G$ is a polycyclic-by-finite group with $\Delta ^{+}(G) = 1$ need not hold in the case of group algebras of finite groups. This turns out to be a purely group theoretic question about the existence of class preserving automorphisms.

References:

[B]
W. Burnside, Theory of Groups of Finite Order, second edition, Cambridge, 1955. MR 16:1086c

[I]
I. M. Isaacs, unpublished note.

[MP1]
S. Montgomery and D. S. Passman, X-inner automorphisms of group rings, Houston J. Math. 7 (1981), 395-402. MR 83d:16038

[MP2]
-, X-inner automorphisms of group rings II, Houston J. Math. 8 (1982), 537-544.MR 84d:16044

[Sh]
C. H. Sah, Automorphisms of finite groups, J. Algebra 10 (1968), 47-68. MR 37:5287

[Sm]
M. K. Smith, Semi-invariant rings, Comm. Algebra 13 (1985), 1283-1298. MR 86g:16018

[Wl]
G. E. Wall, Finite groups with class-preserving outer automorphisms, J. London Math. Soc. 22 (1947), 315-320. MR 10:8g

[Wu]
P. Wauters, The semicentre of a group algebra (to appear in Proc. Edinburgh Math. Soc.).

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Additional Information:

D. S. Passman
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: passman@math.wisc.edu

P. Wauters
Affiliation: Department of Mathematics, Limburgs Universitair Centrum, B-3590 Diepenbeek, Belgium
Email: pwauters@luc.ac.be

DOI: 10.1090/S0002-9939-99-04694-8
PII: S 0002-9939(99)04694-8
Received by editor(s): September 2, 1997
Posted: February 4, 1999
Additional Notes: The first author's research was supported in part by NSF Grant DMS-9622566. The second author's research was supported by an F.W.O.-grant (Belgium). He wishes to thank the Department of Mathematics of the University of Wisconsin-Madison and, in particular, Donald S. Passman and his wife Marjorie for their warm hospitality.
Communicated by: Lance W. Small
Copyright of article: Copyright 1999, American Mathematical Society

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