Semi-invariants and weights of group algebras

of finite groups

Authors:
D. S. Passman and P. Wauters

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1323-1329

MSC (1991):
Primary 16S34, 20D15, 20D45

Published electronically:
February 4, 1999

MathSciNet review:
1476385

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the semi-invariants and weights of a group algebra over a field of characteristic zero. Specifically, we show that certain basic results which hold when is a polycyclic-by-finite group with 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.

**[B]**W. Burnside,*Theory of groups of finite order*, Dover Publications, Inc., New York, 1955. 2d ed. MR**0069818****[I]**I. M. Isaacs, unpublished note.**[MP1]**Susan Montgomery and D. S. Passman,*𝑋-inner automorphisms of group rings*, Houston J. Math.**7**(1981), no. 3, 395–402. MR**640981****[MP2]**Susan Montgomery and D. S. Passman,*𝑋-inner automorphisms of group rings. II*, Houston J. Math.**8**(1982), no. 4, 537–544. MR**688254****[Sh]**Chih-han Sah,*Automorphisms of finite groups*, J. Algebra**10**(1968), 47–68. MR**0229713****[Sm]**Martha K. Smith,*Semi-invariant rings*, Comm. Algebra**13**(1985), no. 6, 1283–1298. MR**788763**, 10.1080/00927878508823219**[Wl]**G. E. Wall,*Finite groups with class-preserving outer automorphisms*, J. London Math. Soc.**22**(1947), 315–320 (1948). MR**0025461****[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:
https://doi.org/10.1090/S0002-9939-99-04694-8

Received by editor(s):
September 2, 1997

Published electronically:
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

Article copyright:
© Copyright 1999
American Mathematical Society