Let $\mathbb{F}_{q}D_{2n}$ be the group algebra of $D_{2n}$, the dihedral group of order $2n$, over $\mathbb{F}_{q}=GF(q)$. In this paper, we establish the structure of $\mathcal{U}(\mathbb{F}_{2^{k}}D_{2n})$, the unit group of $\mathbb{F}_{2^{k}}D_{2n}$ and that of its normalized unitary subgroup $V_{*}(\mathbb{F}_{2^{k}}D_{2n})$ with respect to canonical involution $*$ when $n$ is odd.
A. A. Bovdi and L. Erdei (1996). Unitary units in the modular group algebra of groups of order 16. Technical Reports Debrecen. 96 (4), 57-72 V. A. Bovdi and L. G. Kovacs (1994). Unitary units in modular group algebras. Manuscr. Math.. 84 (1), 57-72 V. Bovdi and A. L. Rosa (2000). On the order of the unitary subgroup of a modular group algebra. Comm. Algebra. 28 (4), 1897-1905 L. Creedon and J. Gildea (2009). Unitary units of the group algebra F2kQ8. Internat. J. Algebra Comput.. 19 (2), 283-289 K. Kaur and M. Khan (2014). Units in F2D2p. J. Algebra Appl., http://dx.doi.org/10.1142/S0219498813500904. 13 (2) R. Lidl and H. Niederreiter (2000). Finite fields. Cambridge University Press, Cambridge. D. J. S. Robinson (1996). A course in the theory of groups. Graduate Texts, Springer-Verlag, New York. 80
Makhijani, N., Sharma, R., & Srivastava, J. B. (2014). Units in F2kd2n. International Journal of Group Theory, 3(3), 25-34. doi: 10.22108/ijgt.2014.4382
MLA
Neha Makhijani; R. Sharma; J. B. Srivastava. "Units in F2kd2n". International Journal of Group Theory, 3, 3, 2014, 25-34. doi: 10.22108/ijgt.2014.4382
HARVARD
Makhijani, N., Sharma, R., Srivastava, J. B. (2014). 'Units in F2kd2n', International Journal of Group Theory, 3(3), pp. 25-34. doi: 10.22108/ijgt.2014.4382
VANCOUVER
Makhijani, N., Sharma, R., Srivastava, J. B. Units in F2kd2n. International Journal of Group Theory, 2014; 3(3): 25-34. doi: 10.22108/ijgt.2014.4382
)
