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Zap. Nauchn. Sem. POMI, 2020, Volume 496, Pages 169–181 (Mi znsl7022)  

The length of the group algebra of the dihedral group of order $2^k$

O. V. Markovaabc, M. A. Khrystika

a Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics
c Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region

Abstract: 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 $2^{k+1} $ over an arbitrary field of characteristic $2$ is equal to $2^{k}$.

Key words and phrases: finite-dimensional algebras, length of an algebra, group algebras, dihedral group.

Funding Agency Grant Number
Russian Science Foundation 17-11-01124


Full text: PDF file (210 kB)
References: PDF file   HTML file
UDC: 512.552
Received: 15.10.2020

Citation: O. V. Markova, M. A. Khrystik, “The length of the group algebra of the dihedral group of order $2^k$”, Computational methods and algorithms. Part XXXIII, Zap. Nauchn. Sem. POMI, 496, POMI, St. Petersburg, 2020, 169–181

Citation in format AMSBIB
\Bibitem{MarKhr20}
\by O.~V.~Markova, M.~A.~Khrystik
\paper The length of the group algebra of the dihedral group of order $2^k$
\inbook Computational methods and algorithms. Part~XXXIII
\serial Zap. Nauchn. Sem. POMI
\yr 2020
\vol 496
\pages 169--181
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7022}


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