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Structure of unitary groups over finite group rings and its application

Jizhu Nan, Yufang Qin (2010)

Czechoslovak Mathematical Journal

In this paper, we determine all the normal forms of Hermitian matrices over finite group rings $R = F_{q^{2}} G$ , where $q = p^{α}$ , $G$ is a commutative $p$ -group with order $p^{β}$ . Furthermore, using the normal forms of Hermitian matrices, we study the structure of unitary group over $R$ through investigating its BN-pair and order. As an application, we construct a Cartesian authentication code and compute its size parameters.

Symplectic K2 of Laurent polynomials, associated Kac-Moody groups and Witt rings.

Ulf Rehmann, Jun Morita (1991)

Mathematische Zeitschrift

The Gersten conjecture for Witt groups in the equicharacteristic case.

Balmer, Paul, Gille, Stefan, Panin, Ivan, Walter, Charles (2002)

Documenta Mathematica

The image of the natural homomorphism of Witt rings of orders in a global field

Beata Rothkegel (2013)

Acta Arithmetica

Let R be a Dedekind domain whose field of fractions is a global field. Moreover, let 𝓞 < R be an order. We examine the image of the natural homomorphism φ : W𝓞 → WR of the corresponding Witt rings. We formulate necessary and sufficient conditions for the surjectivity of φ in the case of all nonreal quadratic number fields, all real quadratic number fields K such that -1 is a norm in the extension K/ℚ, and all quadratic function fields.