Units in finite dihedral and quaternion group algebras

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• 作者：Neha Makhijani ; ^{nehamakhijani@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; R.K. Sharma ^{rksharmaiitd@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; J.B. Srivastava ^{jbsrivas@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Primary ; 16U60 ; Secondary ; 16S34 ; 20C05
• 刊名：Journal of the Egyptian Mathematical Society
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：24
• 期：1
• 页码：5-7
• 全文大小：374 K

文摘

Let F_qG${\mathbb{F}}_{q}G$ be the group algebra of a finite group G   over F_q=GF(q)${\mathbb{F}}_q=\mathit{GF}(q)$. Using the Wedderburn decomposition of 20c2d90aacc25f921c5dbe6f80f0" title="Click to view the MathML source">F_2^kD_2n/J(F_2^kD_2n)${\mathbb{F}}_{2^k}{D}_{2n}/J({\mathbb{F}}_{2^k}{D}_{2n})$, we establish the structure of the unit group of F_2^kG${\mathbb{F}}_{2^k}G$ when G   is either D_4n$D_{4n}$, the dihedral group of order 4n$4n$ or Q_4n$Q_{4n}$, the generalized quaternion group of order 4n,n$4n\text{,}n$ odd.