Group of units of finite group algebras of groups of order 24

• Datum: 2023
• Hauptverfasser: Sahai, M., Ansari, S. F.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2023
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/6680
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 512.5 Let $F$ be a finite field of characteristic $p.$  The structures of the unit groups of group algebras over $F$ of the three groups $D_{24},$ $S_4$ and $SL(2, \mathbb{Z}_3)$ of order $24$  are completely described in numerous works.   We present the unit groups of the group algebras over $F$ for the remaining groups of order $24,$ namely, $C_{24},$ $C_{12} \times C_2,$ $C_2^3 \times C_3,$  $C_3 \rtimes C_8,$  $C_3 \rtimes Q_8,$ $D_6 \times C_4,$ $C_6 \rtimes C_4,$  $C_3 \rtimes D_8,$ $C_3 \times D_8,$  $C_3 \times Q_8,$   $A_4 \times C_2,$ and $D_{12} \times C_2.$