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Solvable Normal Subgroups and Nilpotent Ideals in Matrix Rings.

Charles Lanski (1973)

Mathematische Annalen

Sottogruppi $Q$ -congruenziali di $S L (n, R)$

Remo Gattazzo (1976)

Rendiconti del Seminario Matematico della Università di Padova

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.

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