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.
|Journal||Journal of Algebra and its Applications|
|State||Published - 1 Jul 2022|
Bibliographical noteFunding 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.
© 2022 World Scientific Publishing Company.
- Finite-dimensional algebras
- abelian groups
- group algebras
- lengths of sets and algebras