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Sharma, Rajendra, Yadav, Pooja. (1392). Unit group of algebra of circulant matrices. , 2(4), 1-6. doi: 10.22108/ijgt.2013.2643
Rajendra Sharma; Pooja Yadav. "Unit group of algebra of circulant matrices". , 2, 4, 1392, 1-6. doi: 10.22108/ijgt.2013.2643
Sharma, Rajendra, Yadav, Pooja. (1392). 'Unit group of algebra of circulant matrices', , 2(4), pp. 1-6. doi: 10.22108/ijgt.2013.2643
Sharma, Rajendra, Yadav, Pooja. Unit group of algebra of circulant matrices. , 1392; 2(4): 1-6. doi: 10.22108/ijgt.2013.2643

Unit group of algebra of circulant matrices

International Journal of Group Theory
مقاله 1، دوره 2، شماره 4، اسفند 2013، صفحه 1-6    اصل مقاله (419.53 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2643
نویسندگان
Rajendra Sharma* 1؛ Pooja Yadav2
1Indian Institute of Technology Delhi
2Department of Mathematics, Kamla Nehru College, University of Delhi, Delhi
چکیده
Let $Cr_n(F_p)$ denote the algebra of $n \times n$ circulant‎ ‎matrices over $F_p$‎, ‎the finite field of order $p$ a prime‎. ‎The‎ ‎order of the unit groups $\mathcal{U}(Cr_3(F_p))$‎, ‎$\mathcal{U}(Cr_4(F_p))$ and $\mathcal{U}(Cr_5(F_p))$ of algebras of‎ ‎circulant matrices over $F_p$ are computed‎.
کلیدواژه‌ها
Algebra؛ Unit Group؛ Circulant Matrices
مراجع
V. Bovdi (2001) On symmetric units in group algebras Comm. Algebra 29, 5411-5422
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V. Bovdi and M. M. Parmenter (1997) Symmetric units in integral group rings Publ. Math. Debrecen 50, 369-372
L. Creedon and J. Gildea (2011) The structure of the unit group of the group algebra $\mathbb{F}_{2^k}D_8$ Canad. Math. Bull. 54, 237-243
P. J. Davis (1979) Circulant Matrices Chelsea Publication, New York
J. Gildea (October 2007) Units of Group Algebras PhD Thesis, National University of Ireland, Galway
J. Gildea (2008) The special circulant matrix and units in group rings Acta. Math. Acad. Paedagog. Nyhazi. 24 (2), 221-225
J. Gildea (2008) The order of $\mathcal{U}(F_{2^k}D_{10})$ when $5|(2k-1)$ Int. J. Pure Appl. Math. 49 (4), 525-530
G. Higman (1940) The units of group rings Proc. London Math. Soc. 46 (2), 231-248
T. Hurley (2006) Group rings and rings of matrices Int. J. Pure Appl. Math. 31, 319-335
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