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The extraspecial case of the $k(GV)\;$ problem

Author(s): David Gluck; Kay Magaard
Journal: Trans. Amer. Math. Soc. 354 (2002), 287-333.
MSC (2000): Primary 20C20; Secondary 20C33, 20D06, 20E28
Posted: August 29, 2001
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Abstract: Let $E$ be an extraspecial-type group and $V$ a faithful, absolutely irreducible $k[E]$-module, where $k$ is a finite field. Let $G$ be the normalizer in $GL(V)$ of $E$. We show that, with few exceptions, there exists a $v\in V$such that the restriction of $V$ to $C_H(v)$ is self-dual whenever $H\le G$and $(\vert H\vert, \vert V\vert)=1$.

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Additional Information:

David Gluck
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: dgluck@math.wayne.edu

Kay Magaard
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: kaym@math.wayne.edu

DOI: 10.1090/S0002-9947-01-02839-2
PII: S 0002-9947(01)02839-2
Received by editor(s): August 12, 1999
Received by editor(s) in revised form: January 2, 2001
Posted: August 29, 2001
Additional Notes: Research of both authors partially supported by NSA grants.
Copyright of article: Copyright 2001, American Mathematical Society

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