Units in $F_{2^k}D_{2n}$

Document Type: Research Paper

Authors

1 Indian Institute of Technology Delhi Hauz Khas, New Delhi-110016 India

2 Indian Institute of Technology Delhi Hauz Khas, New Delhi India

Abstract

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.

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