In this paper, the length of the group algebra of a dihedral group in the modular case is computed under the assumption that the order of the group is a power of two. Various methods for studying the length of a group algebra in the modular case are considered. It is proved that the length of the group algebra of a dihedral group of order 2k+1 over an arbitrary field of characteristic 2 is equal to 2k.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 496, 2020, pp. 169–181.
Translated by the authors.
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Markova, O.V., Khrystik, M.A. Length of the Group Algebra of the Dihedral Group of Order 2k. J Math Sci 255, 324–331 (2021). https://doi.org/10.1007/s10958-021-05375-6
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DOI: https://doi.org/10.1007/s10958-021-05375-6