Structure of unitary groups over finite group rings and its application
Czechoslovak Mathematical Journal (2010)
- Volume: 60, Issue: 2, page 495-512
- ISSN: 0011-4642
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topNan, Jizhu, and Qin, Yufang. "Structure of unitary groups over finite group rings and its application." Czechoslovak Mathematical Journal 60.2 (2010): 495-512. <http://eudml.org/doc/38022>.
@article{Nan2010,
abstract = {In this paper, we determine all the normal forms of Hermitian matrices over finite group rings $R=F_\{q^2\}G$, where $q=p^\{\alpha \}$, $G$ is a commutative $p$-group with order $p^\{\beta \}$. 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.},
author = {Nan, Jizhu, Qin, Yufang},
journal = {Czechoslovak Mathematical Journal},
keywords = {finite group ring; BN-pair; authentication code; unitary groups; finite group rings; BN-pairs; authentication codes; normal forms of Hermitian matrices},
language = {eng},
number = {2},
pages = {495-512},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Structure of unitary groups over finite group rings and its application},
url = {http://eudml.org/doc/38022},
volume = {60},
year = {2010},
}
TY - JOUR
AU - Nan, Jizhu
AU - Qin, Yufang
TI - Structure of unitary groups over finite group rings and its application
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 495
EP - 512
AB - In this paper, we determine all the normal forms of Hermitian matrices over finite group rings $R=F_{q^2}G$, where $q=p^{\alpha }$, $G$ is a commutative $p$-group with order $p^{\beta }$. 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.
LA - eng
KW - finite group ring; BN-pair; authentication code; unitary groups; finite group rings; BN-pairs; authentication codes; normal forms of Hermitian matrices
UR - http://eudml.org/doc/38022
ER -
References
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