Unitary groups and ramified extensions

Abstract

We classify all non-degenerate skew-hermitian forms defined over certain local rings, not necessarily commutative, and study some of the fundamental properties of the associated unitary groups, including their orders when the ring in question is finite.

Keywords:

• Local ring
• skew-hermitian form
• unitary group

2010 Mathematics Subject Classifications:

• 15A21
• 15A63
• 11E39
• 11E57
• 20G25

Acknowledgements

We are very grateful to the referee for a thorough reading of the paper and valuable suggestions.