The extraspecial case of the $k(GV)\;$ problem
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- by David Gluck and Kay Magaard
- Trans. Amer. Math. Soc. 354 (2002), 287-333
- DOI: https://doi.org/10.1090/S0002-9947-01-02839-2
- Published electronically: 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 $(\vert H\vert , \vert V\vert )=1$.References
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Bibliographic 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
- MR Author ID: 252279
- Email: kaym@math.wayne.edu
- Received by editor(s): August 12, 1999
- Received by editor(s) in revised form: January 2, 2001
- Published electronically: August 29, 2001
- Additional Notes: Research of both authors partially supported by NSA grants.
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 287-333
- MSC (2000): Primary 20C20; Secondary 20C33, 20D06, 20E28
- DOI: https://doi.org/10.1090/S0002-9947-01-02839-2
- MathSciNet review: 1859277