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arXiv · 1307.0282

Units in $FD_{2p^m}$

Kuldeep Kaur·Manju Khan
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Abstract

In this note, we compute the order and provide the structure of the unit group $\mathcal{U}(FD_{2p^m})$ of the group algebra $FD_{2p^m}$, where $F$ is a finite field of characteristic 2 and $D_{2p^m}$ is the dihedral group of order $2p^m$ such that $p$ is an odd prime. Further, we obtain the structure of the unitary subgroup $\mathcal{U}_*(FD_{2p^m})$ with respect to canonical involution * and prove that it is a normal subgroup of the unit group $\mathcal{U}(FD_{2p^m})$.

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Kuldeep Kaur, Manju Khan. 2013-07-01. Units in $FD_{2p^m}$. https://arxiv.org/abs/1307.0282

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