Group of Units of Finite Group Algebras of Groups of Order 24

2020/05/11 by Meena Sahai, Sahai, Meena, Sheere Farhat Ansari +1
Mathematics · #16S34 #20C05 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16S34 #msc:20C05

paper · pdf · doi:10.48550/arxiv.2005.05014

15 pages

arxiv created 2020/05/11 · arxiv updated 2020/05/12

Abstract

Let F be a finite field of characteristic p. The structures of the unit groups of group algebras over F of the three groups D₂₄, S₄ and SL(2, ℤ₃) of order 24 are completely described in \citeK4, SM, SM1, FM, sh1. In this paper, we give the unit groups of the group algebras over F of the remaining groups of order 24, namely, C₂₄, C₁₂ × C₂, C₂³ × C₃, C₃ \rtimes C₈, C₃ \rtimes Q₈, D₆ × C₄, C₆ \rtimes C₄, C₃ \rtimes D₈, C₃ × D₈, C₃ × Q₈, A₄ × C₂ and D₁₂ × C₂.

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