On the lengths of group algebras of finite abelian groups in the semi-simple case

Alexander Guterman, Olga Markova, Mikhail Khrystik

Research output: Contribution to journalArticlepeer-review


In this paper we solve the problem of finding the length of group algebras of arbitrary finite abelian groups in the case when the characteristic of the ground field does not divide the order of the group. We show that these group algebras have maximal possible lengths for infinite fields and sufficiently large finite fields since they are one-generated. In case of small fields we prove that the length is bounded from above by a logarithmic function of the order of the group.

Original languageEnglish
Article number2250140
JournalJournal of Algebra and its Applications
Issue number7
StatePublished - 1 Jul 2022
Externally publishedYes

Bibliographical note

Funding Information:
The authors are grateful to A. A. Klyachko for the important suggestions on this paper and to the referee for numerous useful comments substantially improving the paper. The investigations of the first and the second authors are supported by Russian Science Foundation Grant 17-11-01124.

Publisher Copyright:
© 2022 World Scientific Publishing Company.


  • Finite-dimensional algebras
  • abelian groups
  • group algebras
  • lengths of sets and algebras


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