Nonexistence of Self-Dual Normal Bases

Abstract

Let G be a finite group of even order. We show that some G-Galois extension L/K has no self-dual normal basis.

Key Words:

• Self-dual normal basis
• Normal basis
• Trace forms

1991 Mathematics Subject Classification:

• 11E04
• 12F05

Acknowledgments

The author would like to thank Z. Reichstein for his help and encouragement. He is also grateful to T.A. Schmidt and the referee for helpful comments on the manuscript.

Notes

^#Communicated by A. Turull.