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

Alexander Guterman; Olga Markova; Mikhail Khrystik

doi:https://doi.org/10.1142/s0219498822501407

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 journal › Article › peer-review

Abstract

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 language	English
Article number	2250140
Journal	Journal of Algebra and its Applications
Volume	21
Issue number	7
DOIs	https://doi.org/10.1142/s0219498822501407
State	Published - 1 Jul 2022
Externally published	Yes

Keywords

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

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Applied Mathematics

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https://doi.org/10.1142/s0219498822501407

Cite this

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abstract = "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.",

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AU - Markova, Olga

AU - Khrystik, Mikhail

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N2 - 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.

AB - 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.

KW - Finite-dimensional algebras

KW - abelian groups

KW - group algebras

KW - lengths of sets and algebras

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JF - Journal of Algebra and its Applications

IS - 7

M1 - 2250140

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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