An example of length computation for a~group algebra of a~noncyclic Abelian group in the modular case

O. V. Markova

Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 2, pp. 217-229.

Résumé

We demonstrate that the technique for calculating the length of two-block matrix algebras, developed by the author earlier, can be used to calculate the lengths of group algebras of Abelian groups. We find the length of the group algebra of a noncyclic Abelian group of order $2p^2 $, where $p> 2$ is a prime number, over a field of characteristic $p$, namely, we prove that the length of this algebra is equal to $3p-2$.

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