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

  • M. Sahai University of Lucknow, India
  • S. F. Ansari University of Lucknow, India
Keywords: Group Algebras, Unit Groups


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 $D_{12} \times C_2.$


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How to Cite
Sahai, M., and S. F. Ansari. “Group of Units of Finite Group Algebras of Groups of Order 24”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 2, Mar. 2023, pp. 215 -29, doi:10.37863/umzh.v75i2.6680.
Research articles