| Title:
|
Structure of unitary groups over finite group rings and its application (English) |
| Author:
|
Nan, Jizhu |
| Author:
|
Qin, Yufang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
495-512 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
finite group ring |
| Keyword:
|
BN-pair |
| Keyword:
|
authentication code |
| MSC:
|
19G24 |
| MSC:
|
20E42 |
| MSC:
|
94A60 |
| idZBL:
|
Zbl 1208.20047 |
| idMR:
|
MR2657964 |
| . |
| Date available:
|
2010-07-20T16:54:04Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140584 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Karpilovsky, G.: Commutative Group Algebra.Marcel Dekker New York (1983). MR 0704185 |
| Reference:
|
[4] Wan, Z. X.: Further construction of Cartesian authentication codes from unitary geometry.Designs, Codes and Cryptology 2 (1992), 333-356. MR 1194775, 10.1007/BF00125202 |
| Reference:
|
[5] Wan, Z. X.: Geometry of Classical Groups over Finite Fields.Studentlitteratur Lund (1993). Zbl 0817.51001, MR 1254440 |
| Reference:
|
[6] You, H.: Sylow subgroups of classical groups over finite commutative rings.Acta Math. Sinica 39 (1996), 33-40 Chinese. Zbl 0863.20020, MR 1412901 |
| Reference:
|
[7] You, H., Nan, J. Z.: Using normal form of matrices over finite fields to construct Cartesian authentication codes.J. Math. Res. Exposition 18 (1998), 341-346. Zbl 0953.94024, MR 1645903 |
| Reference:
|
[8] You, H.: Overgroups of symplectic group in linear group over commutative rings.J. Algebra 282 (2004), 23-32. Zbl 1067.20065, MR 2095570, 10.1016/j.jalgebra.2004.07.036 |
| . |
