# Unit group of algebra of circulant matrices

Document Type: Research Paper

Authors

1 Indian Institute of Technology Delhi

2 Department of Mathematics, Kamla Nehru College, University of Delhi, Delhi

Abstract

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.

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### References

V. Bovdi (2001). On symmetric units in group algebras. Comm. Algebra. 29, 5411-5422
V. Bovdi (2012). Group rings in which the group of units is hyperbolic. J. Group Theory. 15 (2), 227-235
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