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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This research was supported in part by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada, the National Science Foundation of China (11161006, 11171142), the Guangxi Natural Science Foundation (2011GXNSFA018139) and the Guangxi New Century 1000 Talents Project.
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Tang, G., Wei, Y. & Li, Y. Unit groups of group algebras of some small groups. Czech Math J 64, 149–157 (2014). https://doi.org/10.1007/s10587-014-0090-0
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DOI: https://doi.org/10.1007/s10587-014-0090-0