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On a filtered multiplicative basis of group algebras

Victor Bovdi
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Abstract

Let $K$ be a field of characteristic $p$ and $G$ a nonabelian metacyclic finite $p$-group. We give an explicit list of all metacyclic $p$-groups $G$, such that the group algebra $KG$ over a field of characteristic $p$ has a filtered multiplicative $K$-basis. We also present an example of a non-metacyclic 2-group $G$, such that the group algebra $KG$ over any field of characteristic 2 has a filtered multiplicative $K$-basis.

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Victor Bovdi. 2000-09-01. On a filtered multiplicative basis of group algebras. https://arxiv.org/abs/math/0009008

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