In this paper, we address the question of finding the length of group algebras of finite abelian groups in the case when the characteristic of the ground field divides the order of the group. We evaluate the exact length for an arbitrary abelian $p$-group. For other groups we provide upper and lower bounds for the length of their group algebras.

中文翻译：

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关于模情况下有限阿贝尔群的群代数长度

在本文中，我们解决了在基场特征划分群阶的情况下求有限阿贝尔群的群代数长度的问题。我们评估任意阿贝尔的确切长度$p$-团体。对于其他组，我们为其组代数的长度提供上限和下限。