Unit groups of group algebras of some small groups |
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Authors: | Gaohua Tang Yangjiang Wei Yuanlin Li |
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Institution: | 1. School of Mathematical Science, Guangxi Teachers Education University, Nanning, Guangxi, 530001, P.R.China 2. Department of Mathematics, Brock University, St.Catharines, Ontario, Canada, L2S 3A1
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Abstract: | Let FG be a group algebra of a group G over a field F and U (FG) the unit group of FG. It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group G with order 21 over any finite field of characteristic 3 is established. We also characterize the structure of the unit group of FA 4 over any finite field of characteristic 3 and the structure of the unit group of FQ 12 over any finite field of characteristic 2, where Q 12 = 〈x, y; x 6 = 1, y 2 = x 3, x y = x ?1〉. |
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